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

1 Answer
Apr 22, 2018

Answer:

#x = 4, y = 3#

Explanation:

#-2x -3y = -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#