How do you solve the following system?: #-4x -3y =5, x -2y = -15#

1 Answer
May 17, 2018

Answer:

#x = -5 and y = 5#

Explanation:

#-4x- 3y = 5 - - - eqn1#

#x - 2y = -15 - - - eqn2#

From the #eqn1# rearrange the equation..

#-4x - 3y = 5#

Multiplying through by minus#(-)#;

#-(-4x - 3y = 5)#

#4x + 3y = -5 - - - eqn1#

Now solving simultaneously..

#4x + 3y = -5 - - - eqn1#

#x - 2y = -15 - - - eqn2#

Using Elimination Method..

Multiplying #eqn1# by #1# and #eqn2# by #4# respectively..

#1(4x + 3y = -5)#

#4(x - 2y = -15)#

#4x + 3y = -5 - - - eqn3#

#4x - 8y = -60 - - - eqn4#

Subtracting #eqn4# from #eqn3#

#(4x - 4x) + (3y - (-8y) = -5 - (-60)#

#0 + 3y + 8y = -5 + 60#

#11y = 55#

#y = 55/11#

#y = 5#

Substituting the value of #y# into #eqn2#

#x - 2y = -15 - - - eqn2#

#x - 2(5) = -15#

#x - 10 = -15#

#x = -15 + 10#

#x = -5#

Therefore;

#x = -5 and y = 5#