i need help with systems of equations with coefficients?

Question

12y-3y=11

x-2y=-2

Answer 1

Is the first equation supposed to be 12x-3y=11?

If it is, multiply the second equation by 12, and subtract it from the first:

12x-3y=11
12x-24y=-24

21y=35
y=35/21=5/3

substitute the y value into one of the equations:
x-2y=-2
x-2(5/3)=-2
x-10/3=-6/3
x= 4/3

Answer 2

The idea behind solving systems of linear equations is to eliminate all the variables but one such that the value of the last variable is easy to calculate. Sometimes it is not easy to do that, but you are in luck here because this one is easy. Then after finding the value of one variable, we can usually compute the others from the various relationships given in the equations.

In the first equation, there is only one variable, so all you need to do is add together the two terms containing that variable.

12y - 3y = 11
(12 - 3)y = 11
9y = 11
y = 11/9

In the second equation, you have an x value with a coefficient of 1. Now you can say what x is in terms of y. Just transpose -2y to the right side of the equation and factor.

x-2y=-2
x = 2y - 2
x = 2(y - 1).

Since you have already calculated the exact value of y, now all you have to do is plug it into the above to find the exact value of x.

x = 2(11/9 - 1) = 2(11/9 - 9/9) = 2(11 - 9)/ 9 = 2(2)/9 = 4/9.

So x = 4/9.

Now plug your calculated values for x and y into the original equations to see whether those values make the equations true or not. If they do, then we have the right numbers.

Answer 3

In the first example, 12y-3y=11, theres only one variable (y) so simple solve for it.
9y=11
Y=11/9

Now for the second, substitute 11/9 for y.
x-2(11/9)=-2
x(-22/9)=-2
-22/9x=-2
x=18/22

Answer 4

y= 11/9
X plug it in into second one.