Question

Consider the following pair of equations:

x + y = -2
y= 2x + 10

if the two equations are graphed at what point do the lines representing the two equations intersect

Answer 1

The lines representing these equations intercept at the point (-4,2) on the plane.

Explanation:

When we want to find were both lines intercept, we are trying to find a pair of values (x,y) that belongs to both equations, which means that it satisfies both equations at the same time.

Therefore, we can use the second equation that gives us the value of y in terms of x, to substitute for y in the first equation. Then we end up with an equation with a unique unknown, for which we can solve:

`x+y=-2\\x+(2x+10)=-2\\x+2x+10=-2\\3x+10=-2\\3x=-2-10\\3x=-12\\x=(-12)/(3) \\x=-4`

Next we use this value we obtained for x (-4) in the same equation we use for substitution in order to find which y value corresponds to this:

`y=2x+10\\y=2(-4)+10\\y=-8+10\\y=2`

Then we have the pair (x,y) that satisfies both equations (-4,2), which is therefore the point on the plane where both lines intercept.