Question

What is the solution to the system of equations below?

(Hint: Solve using substitution!)

−5x−y=5
x=7y−1
​(

Answer 1

The lines intersect at the point (-1, 0)

Explanation:

−5( )−y=5

-5(7y-1) - y = 5 substitute the x=7y-1 into first equation

-35y + 5 - y =5 multiply -5

-36y + 5 = 5 combine like terms

-36y = 0 subtract 5

y=0 divide by -36

x=7(0)-1 substitute 0 for y in x=7( )-1

=-1 simplify

The lines intersect at the point (-1, 0)

Answer 2

• x = -1, y = 0 or (-1, 0)

Explanation:

We have two equations :

1. -5x - y = 5
2. x = 7y - 1

Take the value of x in Equation 2 and substitute in Equation 1.

• -5(7y - 1) - y = 5
• -35y + 5 - y = 5
• -36y = 0
• y = 0

Now, take the value of y and substitute in Equation 2.

• x = 7(0) - 1
• x = -1

Solution

• x = -1, y = 0 or (-1, 0)