How do you solve –2x – 3y = –17 and x + 4y = 16?

1 Answer
Apr 22, 2018

x = 4, y = 3x=4,y=3

Explanation:

-2x -3y = -172x3y=17

-2x color(red)(cancel(color(black)(-3y)+3y))= -17 color(red)(+3y)

(color(red)(cancel(color(black)(-2)))x)/color(red)(cancel(-2)) = (3y - 17)/color(red)(-2)

x = (3y-17)/-2

____color(white)(.)

x + 4y = 16

x color(red)(cancel(color(black)(+4y)-4y))= 16 color(red)(-4y)

Now we can graph both of these equations on a graph and see where they overlap.

graph{((3y-17)/-2 - x)(- 4y + 16 - x)=0}

These lines overlap at 4, 3

color(blue)(therefore x = 4, y = 3)

To prove this, we can substitute the pronumerlas for their numeric value.

–2x – 3y = –17 , x + 4y = 16

–2 xx 4 – 3 xx 3 = –17 , 4 + 4 xx 3 = 16

–8 – 9 = –17 , 4 + 12 = 16

-17 = –17 , 16 = 16