How do you solve 4x - y = -5 and -2x + 3y = 10?

1 Answer
Sep 6, 2015

Answer:

#{(x=-1/2), (y=3):}#

Explanation:

Your system of equations looks like this

#{(4x-y = -5), (-2x + 3y = 10):}#

Multiply the second equation by #2# to get

#{(4x-y = -5), (-4x + 6y = 20):}#

Notice that if you add the left-hand side of the equations and the right-hand sides of the equations separately, you can eliminate the #x#-term.

This will allow you to find the value of #y#, since you'll be left with one equation with one unknown, #y#.

#{(4x-y = -5), (-4x + 6y = 20):}#
#stackrel("--------------------------------------------")#
#color(red)(cancel(color(black)(4x))) - y - color(red)(cancel(color(black)(4x))) + 6y = -5 + 20#

#5y = 15 implies y = color(green)(3)#

Now take the value of #y# into one of the two original equations to solve for #x#

#4x - 3 = -5#

#4x = -2 implies x = color(green)(-1/2)#