How do you solve 3y=11-2x and 3x=y-11?

1 Answer
Mar 14, 2018

Answer:

Doing some linear algebra, you find that x=-2 and y=5

Explanation:

Set up both equations so y (and coefficients) is alone on the left-hand side (LHS). The first one is already done for you:

#3y=11-2x#
#y=11+3x#

Multiply the second equation by 3, and then subtract equation 2 from equation 1:

#(y=11+3x)*3 rArr 3y=33+9x#

#3y=11-2x#
#-#
#ul(3y=33+9x)#
#0=-22-11x#

Solving for x:

#11x=-22 rArr color(red)(x=-2)#

Now, pick either starting equation and plug in x to solve for y:

#y=11+3x rArr y=11+3(-2)#
#y=11-6 rArr color(blue)(y=5)#