Question 185375
2x-5y=-158
x-y=-40

Your class has been introduced to a system of two equations in two variables.

I will use the substitution method to solve for x and y.  It is one of 4 ways to solve this problem.

You can also solve this question using the following methods:

1-addition method

2-graphing method

3-matrix algebra


2x-5y=-158
x-y=-40


I will isolate x in the equation x - y = -40 and then replace x in the first equation to find the value of y.

x - y = -40

x = y - 40

Now, I will go back to the first equation and plug that value of x.

2(y - 40)-5y = -158

2y - 80 - 5y = -158

-3y - 80 = -158

-3y = 80 - 158

-3y = -78

y = -78/-3

y = 26

I just found the value of y.

Did you see what I did to find y?

We now need to find x.

I will plug that value of y I just found into EITHER of the original equations given and solve for x.

I selected the equation x - y = -40 but I could have chosen the other equation.  It is our choice.

We know that y = 26, right?

So, x - 26 = -40

x = 26 - 40

x = -14

The solution to this system of equations is the point (-14, 26).  It is at this point where the two equations cross or meet on the coordinate plane.

The value of x = -14 and y = 26.

Not bad for a sub teacher, right?