x+y=15 and y=x+3

Question

Please show work, need help badly

Answer 1

Hi Jay,

Once again, the first equation is already in the standard form. (Ax + By = C)

After rearranging the second equation, I get:

-x + y = 3

Notice, this ISN"T true standard form, because we're leading with a negative, but I like it any way.

Notice the coefficients on the x are equal but opposite. (1 and -1)

If I ADD the equations the x's will cancel.

x + y = 15

-x + y = 3

Add them and we get'

2y = 18

y = 9

We're half done.

We still need to find x.

Substitute 9 for y in either equation and solve for x.

I'm going to use the second equation because the numbers are smaller.

9 = x + 3

x = 6

The point of intersection is (6, 9)

I hope this helps.

Answer 2

the two equations are graphically perpendicular lines

they have slopes that are 1 and -1. those numbers are negative inverses of each other.

the two perpendicular lines intersect at (6,9)

one line is upward sloping at a 45 degree angle

the other is downward sloping a -45 degrees with the x axis