Question

Consider the following pair of equations: y = x + 4 y = −5x − 2 Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answer 1

(- 1, 3 )

Explanation:

Given the 2 equations

y = x + 4 → (1)

y = - 5x - 2 → (2)

Substitute y = x + 4 into (2)

x + 4 = - 5x - 2 ( add 5x to both sides )

6x + 4 = - 2 ( subtract 4 from both sides )

6x = - 6 ( divide both sides by 6 )

x = - 1

Substitute x = - 1 into either of the 2 equations and evaluate for y

Substituting into (1)

y = - 1 + 4 = 3

solution is (- 1, 3 )

Answer 2

(-1, 3)

Explanation:

to solve using substitution, you have to know the value of either x or y. in this example, they gave you the value of y already: y=x+4.

this means you can substitute the y for (x+4). if we substitute y for (x+4) in the equation y=-5x-2, we get this:

(x+4)=-5x-2

then solve for x

6x=-6

so x=-1

since we know the x value, we can solve for y

y=x+4

y=-1+4

y=3

so the final answer is (-1, 3)