How do you solve 4x-y =104xy=10, 3x+5y=193x+5y=19 by graphing and classify the system?

1 Answer
Jan 22, 2018

color(blue)(x= 3," " y =2)x=3, y=2

Explanation:

Given:

4x-y=10" "4xy=10 color(red)(Equation.1Equation.1

3x+5y=19" "3x+5y=19 color(red)(Equation.2Equation.2

Analyze the graph below for the solution:

enter image source here

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

color(blue)(x= 3," " y =2)x=3, y=2

satisfies the system of linear equations:

4x-y=10" "4xy=10 color(brown)(Equation.1Equation.1

3x+5y=19" "3x+5y=19 color(brown)(Equation.2Equation.2

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

4(3)-2=10" "4(3)2=10 color(green)(Equation.1Equation.1

3(3)+5(2)=19" "3(3)+5(2)=19 color(green)(Equation.2Equation.2

Hence verified.