# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 3x - 2y = 10 and 5x + 2y = 6?

Jul 19, 2018

The lines intersect at a single point, therefore the system of equations is consistent.

#### Explanation:

Equation 1: $3 x - 2 y = 10$

Equation 2 : $5 x + 2 y = 6$

Both equations are in the standard form for a linear equation. This form makes it easy to determine the x- and y-intercepts. We can use those two points to graph each equation.

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

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

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

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

Equation 1

$3 x - 2 y = 10$

X-intercept: Substitute $0$ for $y$ and solve for $x$.

$3 x - 2 \left(0\right) = 10$

$3 x = 10$

Divide both sides by $3$.

$x = \frac{10}{3}$ or $\approx 3.333$

x-intercept: $\left(\frac{10}{3} , 0\right)$ or $\left(\approx 3.333 , 0\right)$ Plot this point.

Y-intercept: Substitute $0$ for $x$ and solve for $y$.

$3 \left(0\right) - 2 y = 10$

$- 2 y = 10$

Divide both sides by $- 2$.

$y = \frac{10}{- 2}$

$y = - 5$

y-intercept: $\left(0 , - 5\right)$ Plot this point.

Draw a straight line through the two points. This is the graph for Equation 1.

Equation 2

$5 x + 2 y = 6$

X-intercept: Substitute $0$ for $y$ and solve for $x$.

$5 x + 2 \left(0\right) = 6$

$5 x = 6$

Divide both sides by $5$.

$x = \frac{6}{5}$ or $1.2$

x-intercept: $\left(\frac{6}{5} , 0\right)$ or $\left(1.2 , 0\right)$ Plot this point.

Y-intercept: Substitute $0$ for $x$ and solve for $y$.

$5 \left(0\right) + 2 y = 6$

$2 y = 6$

Divide both sides by $2$.

$y = \frac{6}{2}$

$y = 3$

y-intercept: $\left(0 , 3\right)$ Plot this point.

Draw a line between the two points. This is the graph of Equation 2.

The lines intersect at a single point, therefore the system of equations is consistent.

graph{(3x-2y-10)(5x+2y-6)=0 [-10, 10, -5, 5]}