# How do you solve the system of equations by graphing 9x - 7y = -42 and 7y - 9x = 42 and then classify the system?

May 21, 2018

The solution for a system of linear equations is the point or points that they have in common. Because both equations represent the same line, they have all points in common, so there are an infinite number of solutions.

#### Explanation:

Solve system of linear equations by graphing:

$\text{Equation 1} :$ $9 x - 7 y = - 42$

$\text{Equation 2} :$ $7 y - 9 x = 42$

The equations are the same.

Multiply Equation 2 by $- 1$. This will reverse the signs.

$- 7 y + 9 x = - 42$

Rearrange $- 7 y$ and $9 x$.

$9 x - 7 y = - 42$

To graph the lines, determine the x- and y-intercepts.

X-intercept: value of $x$ when $y = 0$

Substitute $0$ for $y$ and solve for $x$.

$9 x - 7 \left(0\right) = - 42$

$9 x = - 42$

Divide both sides by $9$.

$x = - \frac{42}{9}$

The x-intercept is $\left(- \frac{42}{9} , 0\right)$ or $\approx \left(- 4.667 , 0\right)$.

Y-intercept: value of $y$ when $x = 0$

Substitute $0$ for $x$ and solve for $y$.

$9 \left(0\right) - 7 y = - 42$

$- 7 y = - 42$

Divide both sides by $- 7$.

$y = \frac{- 42}{- 7}$

$y = 6$

The y-intercept is $\left(0 , 6\right)$.

Plot the intercepts and draw a straight line through both points.

The solution for a system of linear equations is the point or points that they have in common. Because both equations represent the same line, they have all points in common, so there are an infinite number of solutions.

graph{(9x-7y+42)(7y-9x-42)=0 [-10, 10, -5, 5]}