Question

Consider the following pair of equations:

y = x + 4
y = −2x − 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

y=x+4 and y=-2x-2 When they are equal it follows that y=y at that point as well so we can say:

x+4=-2x-2 add 2x to both sides

3x+4=-2 subtract 4 from both sides

3x=-6 divide both sides by 3

x=-2, now we can use this value in either original equation to solve for y...

y=x+4 becomes:

y=-2+4

y=2

So the solution, or the point graphically where these lines intersect is:

(-2, 2)