Question

How do you solve this system of equations: `2x - 6y = 14 and x - 2y = 5`?

Answer 1

Point of intersection: `(1,-2)`

Refer to the explanation for the process.

Explanation:

Solve system of equations:

Equation 1: `2x-6y=14`

Equation 2: `x-2y=5`

The equations are linear equations in standard form. The values for `x` and `y` make up the point of intersection of the two lines. The method I will use is substitution.

Solve Equation 2 for `x`.

`x=5+2y`

Substitute `5+2y` for `x` in Equation 1 and solve for `y`.

`2(5+2y)-6y=14`

Expand.

`10+4y-6y=14`

Subtract `10` from both sides.

`4y-6y=14-10`

Simplify both sides.

`-2y=4`

Divide both sides by `-2`.

`y=4/(-2)`

Simplify.

`y=-4/2`

`y=-2`

Substitute `-2` for `y` in Equation 2 and solve for `x`.

`x-2(-2)=5`

Simplify.

`x+4=5`

`x=5-4`

`x=1`

Point of intersection: `(1,-2)`