O solve this system of equations by addition, what could you multiply each equation by to cancel out the x-variable? A: 5x - 2y = 10 B: 4x + 3y = 7

1 Answer
Mar 27, 2016

Answer:

Multiply #5x-2y=10# by #4#.
Multiply #4x+3y=7# by #5#.

Explanation:

In order to cancel out the #x# variable, the coefficient of #x# in both equations must be equal. Thus, find the L.C.M. (lowest common multiple) of #4# and #5#, which is #20#.

For #5x-2y=10#, in order to make the coefficient of #5x# be #20#, the whole equation must be multiplied by #4#.

#4(5x-2y=10)#

#color(darkorange)("Equation"color(white)(i)1)#: #20x-8y=40#

Similarly, for #4x+3y=7#, in order to make the coefficient of #4x# be #20#, the whole equation must be multiplied by #5#.

#5(4x+3y=7)#

#color(darkorange)("Equation"color(white)(i)2#: #20x+15y=35#

Since elimination works by subtracting one equation from the other, if you try subtracting equation #2# from equation #1#, the terms with #x# will become #color(blue)("zero")#.

#color(white)(Xx)20x-8y=40#
#(-(20x+15y=35))/(color(blue)(0x)-23y=5)#