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

1 Answer
Jan 22, 2018

Answer:

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

Explanation:

Given:

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

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

satisfies the system of linear equations:

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

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

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

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

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

Hence verified.