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

1 Answer
Meave60
Mar 18, 2018

The point of intersection is #(2,1/2)#.

Explanation:

Solve system of equations:

#"Equation 1":# #3x-2y=5#

#"Equation 2":# #x+4y=4#

The two equations are linear equations in standard form. The solved values for #x# and #y# will be the point of intersection of the two lines.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve Equation 2 for #x#.

Subtract #4y# from both sides of the equation.

#x=4-4y#

Substitute #(4-4y)# for #x# in Equation 1 and solve for #y#.

#3(4-4y)-2y=5#

Expand.

#12-12y-2y=5#

Simplify.

#12-14y=5#

Subtract #12# from both sides of the equation.

#-14y=5-12#

Simplify.

#-14y=-7#

Divide both sides by #-14#.

#y=(-7)/(-14)#

Simplify.

#y=1/2#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute #1/2# for #y# in Equation 2 and solve for #x#.

#x+4(1/2)=4#

#x+cancel4^2(1/cancel2^1)=4#

Simplify.

#x+2=4#

Subtract #2# from both sides.

#x=4-2#

Simplify.

#x=2#

The point of intersection is #(2,1/2)#.

https://www.wolframalpha.com/input/?i=solve+system+:+3x-2y%3D5,+x%2B4y%3D4

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