How do you find an ordered pair for 2x-3y=7 and -3x+y=7?
1 Answer
Explanation:
You are trying to find a single point that will satisfy both equations. In other words, the solution is the point where these two lines cross.
There are several methods you can use to solve this system of two equations and two variables. In this case, substitution may be easiest:
-
Rewrite the second equation to "solve for
y ":
-3x+y=7
-3x color(red)( + 3x)+y=7 color(red)( + 3x)
color(blue)(y=3x+7) -
Substitute
color(blue)(3x+7) fory in the first equation:
2x-3y=7
2x-3(color(blue)(3x+7))=7 -
Expand and simplify
2x-3(3x+7)=7
2x-color(red)(9x-21)=7
color(red)(-7x)-21=7 -
Solve for
x
-7x-21color(red)(+21)=7color(red)(+21)
-7x=color(red)(28)
(-7x)/color(red)(-7)=28/color(red)(-7)
(cancel(-7)x)/cancel(-7)=color(red)(-4)
color(blue)(x=-4) -
Substitute
color(blue)(x=-4) into one of the equations to findy . Let's use the form we found in Step 1
y=3x+7
y=3(color(red)(-4))+7
y=color(red)(-12)+7
color(blue)(y=-5)
Our solution is
CHECK
Plug the solution into the original equations to make sure they work