# How do you solve 4x-y =10, 3x+5y=19 by graphing and classify the system?

Jan 22, 2018

$\textcolor{b l u e}{x = 3 , \text{ } y = 2}$

#### Explanation:

Given:

$4 x - y = 10 \text{ }$color(red)(Equation.1

$3 x + 5 y = 19 \text{ }$color(red)(Equation.2

Analyze the graph below for the solution:

If the graphs of the equations intersect, then there is one solution that is true for both equations.

When a system has one solution (the graphs of the equations intersect once), the system is a consistent system of linear equations and the equations are independent.

We can observe that our solution

$\textcolor{b l u e}{x = 3 , \text{ } y = 2}$

satisfies the system of linear equations:

$4 x - y = 10 \text{ }$color(brown)(Equation.1

$3 x + 5 y = 19 \text{ }$color(brown)(Equation.2

Plug the values of color(blue)(x=3, " "y=2" " above to verify.

$4 \left(3\right) - 2 = 10 \text{ }$ color(green)(Equation.1

$3 \left(3\right) + 5 \left(2\right) = 19 \text{ }$ color(green)(Equation.2

Hence verified.