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

Aug 12, 2017

The point of intersection is $\left(6 , - 1\right)$ #### Explanation:

Solve system of equations:

These are linear equations in standard form $\left(A x + B y = C\right)$, 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": $x - 2 y = 8$

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

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

Subtract $8 + 2 y$ from both sides.

$x = 8 + 2 y$

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

$2 \left(8 + 2 y\right) + 3 y = 9$

Expand.

$16 + 4 y + 3 y = 9$

Subtract $16$ from both sides.

$4 y + 3 y = 9 - 16$

Simplify.

$7 y = - 7$

Divide both sides by $7$.

$y = \frac{- 7}{7}$

$y = \textcolor{b l u e}{- 1}$

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

$x - 2 \left(- 1\right) = 8$

Simplify.

$x + 2 = 8$

Subtract $2$ from both sides.

$x = 8 - 2$

$x = \textcolor{red}{6}$

The point of intersection is: $\left(\textcolor{red}{6} , \textcolor{b l u e}{- 1}\right)$ 