Hello Assalamualaikum warahmatullahi wabarakatuh, back again with Mrs. Husnul this time in the compulsory Mathematics lesson for grade 10 today we learn about the system of linear equations of two variables. Well, previously, what is a system of linear equations of two variables? Well, actually, we have studied this material in junior high school grade 8 Allah's calendar. So, a system of linear equations of two variables is a system or collection of two or more linear equations of two variables with a power of one and are related to each other so that there is one solution. So, to be stemmed together with Z2, the variable has two or more equations. However, these two or more equations are related to each other so that later the solution will only be there now. Rasayan, which of the following equations is a linear equation of two variables? Well, the first is 3 x squared + 5 y = 6. Is this a linear equation of two variables? Hi, the answer is not a linear equation of two variables because why here the highest power of the variable is a power of two. Well, for a linear equation of two linear variables here, it means the highest power is power-1, meaning if there is a power of two like this, it means it is not a linear equation of two variables. Well, continue with 3P Add 5C minus R = 7 Now is this a linear equation of two variables no yes This is also not a linear equation of two variables because why here there are three variables there are P Q and R well these are three variables so this is not a linear equation of two variables well 2x minus 3 y = 9 Is this a linear equation of two variables consisting of two variables and linear or power of the variable = Hi that is a linear equation of two variables Well can all Ananda verses generally distinguish which linear equation of two variables and which is not a linear equation of two variables Well we continue the general form of a linear equation of two variables so the general form of a linear equation of two variables is ABS + b y = c to be a and b are the coefficients of X and Y are variables C It is a constant yes so the variables are X and y a is the coefficient of X B is the coefficient of y and C is a constant okay then What is the general form of a system of linear equations of two variables Well so if for example it is already in the form of a system and Ih there are two equations and these are related to each other and so the general form is a is X + B one y = c 1 Oh a x + B 2y = C2 to be aa1 B1 c1rca two B2 and c 2 are real numbers, so if there are two equations like this because this is a system, then there will only be a value for X and there is only one value for yes, yes, there is one solution. So next we go to the example question. Determine the solution of the following system of equations x + 3y = 7 x minus 6 y = Min 11, so if it's like this, So the first one we consider as the first equation, yes, the second one we consider as the second equation, it becomes a step to solve the system of linear equations in two variables. We first determine whether we want to eliminate X or Y. Hi, which is younger, which is younger to make the coefficients the same, if there are already the same ones, then that is what is eliminated. Well, because here we see that both the X coefficients in the first equation are one, the X coefficients in the second equation are one, meaning we can immediately eliminate the X coefficient, yes, we eliminate the x variable, yes, Sorry, eliminate the x variable because the coefficients are already the same, so X + 3y = 7 x minus 6 y = Min 9, this is okay, yes, we eliminate, meaning we use the minus sign because so that this x is worth 0 x minus X right X minus X the result is zero yes Then 3 Y minus minus 6y yes 3 Y minus minus 6y means MP3 minus 6 means the same if we write three plus 6 y because minus with minus meets it becomes positive so here it is 9 y = then this 7 minus 11 minus here minus here also means 7 plus 11 the result is 18 so the value is 18/9 so Y = 2 if we have got one of the values ​​here we choose whether we want the first equation or the second equation we enter the value Y = 2 here yes so substitute the value of y into one of the equations you can choose the first person to the second equation it will be the same you just choose the one that is a bit small so you don't get too confused calculating yes so here we just choose the first one X + 3y with seven now we want to find the value of x yes that means there is no value yet what we have is only the value of y y is equal to two means we replace it here with two so x + 3 times 2 = 7 so the exchange just goes down 7 on the right side also goes down it doesn't matter what is replaced is just this one yes replaced with two occurs x + 6 three times 26 x + 6 = 7 earlier x = 7 minus six positive 6 move to the right side so negative 6 so X = 761 Okay we have got the value of x and the value of y so the solution is x = 1 and Y = 2C How can you understand so the first step is to first determine which one to eliminate rx1y if there is already the same coefficient like this, it means we immediately eliminate the x variable okay now let's go to the second example question Determine the solution of the following system of equations x minus y = 2 2 x + 3y = 19 So x minus y = 2 we consider as the first equation 2 x + 3y = 19 we consider as the second equation Well if it's like this if the problem is like this well up to the first one we determine which one we want to eliminate Is X the x variable or the variable well first let's see if there is any the coefficient is the same variable x or Y no yes here to coincide first coefficient xx1 in the second equation the coefficient x is two for the Y in the first equation I visionex it is ecoefficient only that Min Hai coefficient Yedi second equation is positive 3 there is no same means what we have to do we have to make the coefficient the same so we choose first here in this video Mom wants to eliminate the y again yes earlier in the first example question Mom gave an example to eliminate the X variable x Karang Eh mom wants to eliminate the variable y Well so to eliminate the variable y then means the first one must be three yes Because to follow the second equation yes means if we have to multiply the first equation by three yes multiply the first equation by three Why must it be by three so that later this coefficient will be worth 3 yes after multiplying because we want to equate it with the coefficient y in the second equation then equation 2 just multiply by 1 because later after the first one is multiplied by three it will be the same as the coefficient in the second equation so that we get nah x minus y = 2 this was the first equation multiplied by three means x * three get 3x Min y times three get Min 3y two times three the result is 6 well the second equation is multiplied by 100 it remains the same yes 2 x + 3y = 19 Well if it is like this it is ready to eliminate the Y variable to eliminate the y variable 3 X minus 3 Y = 6 this is yes after being multiplied by three Then we use the plus sign Well why not a minus sign because here if for example we use a minus sign it means minus 3 Y minus 3 Y Well that doesn't appear not finished not eliminated the variable in the result if min 3 Y minus three is min 6 y min 3 minus three gets min 6 so we have to use here the plus sign because minus 3y + positive 3y yes min 3 plus three is zero It means the variable is finished for the y variable then for x3x + 2x the result is 5X 6 Plus 19 gets 25 so the x value is equal to 25/5 the result is five well when we have got the x value we choose which one we want substitute into the first equation or the second equation which is easier which is not too difficult you calculate the writing again yes the first Let's just substitute the first equation x minus y = 2 from here we have got the value of x y = 5 which means Five minus y = 2 Well so if this yee goes down don't just Yes yes this is one package with this sign in front so min y yes this is down Min Y = 2 on the right side goes down five on the left side This moves to the right side so it's negative because five This is positive 5 then moves to the right side so it's negative 5 so minus Y = 2 minus 5 min 3 yes so minus y = min 3 the name sing each multiplied by negative the result is y = 3 so we have got the solution x = 5 and Y = 3 well how about it enough easy enough to be an example of the first question earlier, the mother explained that in the question there are already the same coefficients yes the same variable coefficients mean just eliminate Well for this second example question if there are no the same coefficients yes it doesn't mean we have to determine first which one to eliminate variable x or variable y if we have determined it Well, let's try to localize the first equation with how many the second equation with how many so that the variables we want to eliminate can be finished okay that's all for today Assalamualaikum warahmatullahi wabarakatuh [ Music] like