How do you solve the following system using substitution?: 3x - 2 y = 5, x+ 4 y = 43x−2y=5,x+4y=4

1 Answer
Meave60
Mar 18, 2018

The point of intersection is (2,1/2)(2,12).

Explanation:

Solve system of equations:

"Equation 1":Equation 1: 3x-2y=53x−2y=5

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

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

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Solve Equation 2 for xx.

Subtract 4y4y from both sides of the equation.

x=4-4yx=4−4y

Substitute (4-4y)(4−4y) for xx in Equation 1 and solve for yy.

3(4-4y)-2y=53(4−4y)−2y=5

Expand.

12-12y-2y=512−12y−2y=5

Simplify.

12-14y=512−14y=5

Subtract 1212 from both sides of the equation.

-14y=5-12−14y=5−12

Simplify.

-14y=-7−14y=−7

Divide both sides by -14−14.

y=(-7)/(-14)y=−7−14

Simplify.

y=1/2y=12

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Substitute 1/212 for yy in Equation 2 and solve for xx.

x+4(1/2)=4x+4(12)=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](https://d2jmvrsizmvf4x.cloudfront.net/nPUtiPmRHBEkgdQdQEw2_gif%26s%3D39)

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