Question

How do you solve `3x - 7y = 27` and `- 5x + 4y = - 45` using substitution?

Answer 1

The solution is `(9,0)`.

Explanation:

Solve the system of equations:

`"Equation 1":` `3x-7y=27`

`"Equation 2":` `-5x+4y=-45`

These are two linear equations in standard form. The solution to the system is the point they have in common, which is the point where they intersect.

Solve Equation 1 for `x`.

`3x-7y=27`

Add `7y` to both sides of the equation.

`3x=7y+27`

Divide both sides by `3`.

`x=7/3y+27/3`

`x=7/3y+9`

Substitute `7/3y+9` for `x` in Equation 2 and solve for `y`.

`-5x+4y=-45`

`-5(7/3y+9)+4y=-45`

Expand.

`-35/3y-45+4y=-45`

Simplify `-35/3y` to `(-35y)/3`.

Add `45` to both sides.

`(-35y)/3+4y=-45+45`

`(-35y)/3+4y=0`

Multiply `4y` by `3/3` to get an equivalent fraction with `3` as the denominator.

`(-35y)/3+4yxx3/3=0`

`(-35y)/3+(12y)/3=0`

Simplify.

`(-23y)/3=0`

Multiply both sides by `3`.

`-23y=0xx3`

`-23y=0`

Divide both sides by `-23`.

`y=0/(-23)`

`y=0`

Substitute `0` for `y` in Equation 1 and solve for `x`.

`3x-7y=27`

`3x-7(0)=27`

`3x=27`

Divide both sides by `3`.

`x=27/3`

`x=9`

The solution is `(9,0)`.

graph{(3x-7y-27)(-5x+4y+45)=0 [-10, 10, -5, 5]}