How do you solve linear system? Such as -3x+2y +-13 , -2x-3y=-13

Question

Algebra 2 question.

Answer 1

I'm assuming that your first equation should read, "-3x+2y=-13," not "-3x+2y+-13."

 

These must be solved as simultaneous equations.

 

In order to solve, you must first eliminate one variable or the other (either x or y).  You do this by multiplying both sides of both equations simultaneously by a constant such that, when the two equations are added together, one of the variables drops out.  Here's how:

 

{1} Place your equations one on top of the other

 

-3x + 2y = -13

-2x  - 3y = -13

 

 

{2} For the purposes of this example, we will work to eliminate "x" and first solve for "y."  We will multiply both sides of the top equation by 2, and both sides of the bottom equation by -3.  This will set both equations up so that we can get rid of the expressions containing "x."

 

(2)  -3x + 2y = -13 (2)   --->   -6x + 4y = -26

(-3) -2x - 3y = -13 (-3)  --->  +6x + 9y = +39

 

 

{3} We now add the x-containing expressions, the y-containing expressions, and the constants on the other side of the equations to come up with an equation that we can solve for "y".

 

 -6x + 4y = -26     (Add -6x and +6x to eliminate x's, add 4y and 9y to get 13y, and add -26 and +39 to get 13)

+6x + 9y = +39

  0x + 13y = 13  --->  13y = 13

 

Therefore, y=1

 

{4} Now, we should be able to plug that "y=1" into EITHER of the original equations, and we should arrive at the SAME value for "x" in either case.  Let's try:

 

Equation #1: -3x + 2y = -13

                      -3x + 2(1) = -13

                      -3x + 2 = -13

                      -3x = -15

                         x = 5

 

Equation #2: -2x - 3y = -13

                      -2x - 3(1) = -13

                      -2x - 3 = -13

                      -2x = -10

                         x = 5

 

Therefore, for this pair of equations, x=5 and y=1.