Question

How do you solve this system of equations: `2x + 6y = 12; 10y - 3x = 15`?

Answer 1

The point of intersection is `(15/19,33/19)`.

Refer to the explanation for the process.

Explanation:

Solve the system of equations:

`2x+6y=12` `color(white)(...)andcolor(white)(...)` `10y-3x=15`

These are linear equations. The procedure will be to solve for `x` and `y` by substitution. The resulting values for `x` and `y` represent the point of intersection between the two lines.

First Equation: `2x+6y=12`

Solve for `x`.

Subtract `6y` from both sides.

`2x=12-6y`

Divide both sides by `2`.

`x=6-3y`

Second Equation: `10y-3x=15`

Substitute `6-3y` for `x`.

`10y-3(6-3y)=15`

Expand.

`10y-18+9y=15`

Add `18` to both sides.

`10y+9y=15+18`

Simplify.

`19y=33`

Divide both sides by `19`.

`y=33/19`

Go back to the first equation and substitute `33/19` for `y`. Solve for `x`.

`2x+6(33/19)=12`

`2x+198/19=12`

Subtract `198/19` from both sides.

`2x=12-198/19`

Multiply `12` by `19/19`.

`2x=(12xx19)/(1xx19)-198/19`

Simplify.

`2x=228/19-198/19`

Simplify.

`2x=30/19`

Divide both sides by `2`.

`x=30/19-:2`

Simplify.

`x=30/19xx1/2`

Simplify.

`x=30/38`

Reduce the fraction.

`x=(30-:2)/(38-:2)`

`x=15/19`

The point of intersection is `(15/19,33/19)`.