How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent y = -3x - 7 and -8x + 2y = 1?

Jul 12, 2018

The solution is $\left(- \frac{15}{14} , - \frac{53}{14}\right)$ or $\approx \left(- 1.07 , - 3.79\right)$. Since there is one solution, the system is consistent.

Explanation:

Equation 1: y=-3x-7

Equation 2: -8x+2y=1

Equation 1 is already solved for $y$. Substitute $- 3 x - 7$ for $y$ in Equation 2 and solve for $x$.

$- 8 x + 2 \left(- 3 x - 7\right) = 1$

Expand.

$- 8 x - 6 x - 14 = 1$

Add $14$ to both sides.

$- 8 x - 6 x = 1 + 14$

Simplify.

$- 14 x = 15$

Divide both sides by $- 14$.

$x = - \frac{15}{14}$ or $\approx - 1.07$

Substitute $- \frac{15}{14}$ for $x$ in Equation 1 and solve for $y$.

$y = - 3 \left(- \frac{15}{14}\right) - 7$

Expand.

$y = \frac{45}{14} - 7$

Multiply $7$ by $\frac{14}{14}$ to get an equivalent fraction with $14$ as the denominator. Since $\frac{n}{n} = 1$, the numbers will change, but not the value.

$y = \frac{45}{14} - \left(7 \times \frac{14}{14}\right)$

Simplilfy.

$y = \frac{45}{14} - \frac{98}{14}$

Simplify.

$y = - \frac{53}{14}$ or $\approx 3.79$

The solution is $\left(- \frac{15}{14} , - \frac{53}{14}\right)$ or $\approx \left(- 1.07 , - 3.79\right)$. Since there is one solution, the system is consistent.

graph{(y+3x+7)(-8x+2y-1)=0 [-10, 10, -5, 5]}