Question

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

Answer 1

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.

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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`

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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)`.