Question

For the following system, use the second equation to make a substitution for x in the first equation.

x + 5y - 10 = 0
x = 2y - 8
What is the resulting equation in simplest form?

Answer 1

x + 5y - 10 = 0
x = 2y - 8

Substitute the value of x in the 2nd equation to the 1st equation.

2y - 8 + 5y - 10 = 0
7y - 18 = 0 This is the resulting equation in its simplest form.

Find the value of y to get the corresponding value of x.

7y -18 = 0
7y = 18
y = 18/7
y = 2 4/7

x = 2y - 8
x = 2 (18/7) - 8
x = 36/7 - 8
x = 36/7 - (8 * 7/7)
x = 36/7 - 56/7
x = (36-56)/7
x = -20/7
x = -2 6/7

to check:
x + 5y - 10 = 0
-20/7 + 5(18/7) - 10 = 0
-20/7 + 90/7 - 10 = 0
-20/7 + 90/7 - (10 * 7/7) = 0
-20/7 + 90/7 - 70/7 = 0
(-20+90-70)/7 = 0
0/7 = 0
0=0