# algebra

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how do you use the substitution method to solve the linear system?
-2x-5y=7
7x=y=-8

• algebra -

Is the second line supposed to be 7x + y = -8, or 7x - y = -8? You sweem to have inserted a second equal sign by mistake.

Whichever it is, use the second equation to derive an equation for y in terms of x. Then substitute that "y" value into the first equation, and it will be an equation in x only. Solve it.

• algebra -

7x+y=-8
i don't understand what you mean. could you possibly do an example?

• algebra -

We have this:

How do you use the substitution method to solve the linear system?

-2x - 5y = 7...Equation A

7x - y = -8...Equation B

The idea is to isolate y OR x (your choice) and then plug that into EITHER Equation A or B (your choice).

I will isolate y in Equation B.

7x - y = -8...Equation B

-y = -7x - 8

y = (-7x - 8)/-1

y = 7x + 8

Do you see that we NOW know that y is 7x + 8?

To find x, I will plug 7x + 8 into EITHER Equation A or B.

I will choose Equation A.

-2x-5y = 7...Equation A

-2x - 5(2x + 8) = 7

-2x - 10x - 40 = 7

-12x - 40 = 7

-12x = 7 + 40

-12x = 47

x = 47/-12

x = -47/12...Value for x.

We just found the value of x and it is
-47/12. See it above?

We now plug our value for x into EITHER Equation A or B to find the value of y.

I will choose Equation A again.

-2x -5y = 7...Equation A

-2(-47/12) - 5y = 7

47/6 - 5y = 7

-5y = -47/6 + 7

-5y = -5/6

y = -5/6 divided by -5

y = 1/6

The solution for this system of linear equations in two variables is
x = -47/12 and y = 1/6.

We can also write the solution this way:

(-47/12, 1/6) = (x, y), where x represents -47/12 and y represents 1/6.

Done!

• algebra -

7x+y=-8

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