Question

Which graph shows the solution to the system of equations `x-2y=8` and `2x+3y=9`?

Answer 1

The point of intersection is `(6,-1)`


Explanation:

Solve system of equations:

These are linear equations in standard form `(Ax+By=C)`, and can be solved by substitution. The resulting `x` and `y` values represent the intersection of the two lines on a graph.

`color(red)("Equation 1":` `x-2y=8`

`color(blue)("Equation 2":` `2x+3y=9`

I'm going to start with the `color(red)("Equation 1"` and solve for `x`, because its the simplest equation.

Subtract `8+2y` from both sides.

`x=8+2y`

Now solve for `y` in `color(blue)("Equation 2"` by substituting `8+2y` for `x`.

`2(8+2y)+3y=9`

Expand.

`16+4y+3y=9`

Subtract `16` from both sides.

`4y+3y=9-16`

Simplify.

`7y=-7`

Divide both sides by `7`.

`y=(-7)/7`

`y=color(blue)(-1)`

Now substitute `-1` for `y` in `color(red)("Equation 1"` and solve for `x`.

`x-2(-1)=8`

Simplify.

`x+2=8`

Subtract `2` from both sides.

`x=8-2`

`x=color(red)6`

The point of intersection is: `(color(red)6,color(blue)(-1))`