Answer:
(-5, 8)
Step-by-step explanation:
There are three ways to solve a system of equations, graphing, substitution, and elimination. Elimination is not possible in this case because adding or subtracting both equations won't leave us with a single variable equation.
Method 1: graphing
Arguably the easiest method when solving a system of equations, just plug in the equations in a graphing calculator and check at which point they intersect.
(See picture)
Both lines intersect at the point (-5, 8).
Method 2: elimination
Start by choosing any of the two equations and isolating any of the two variables:
[tex]6x+5y=10\\5y=10-6x\\y=2-\frac{6}{5}x[/tex]
Replace the isolated variable into the other equation:
[tex]-2x-3(2-\frac{6}{5}x)=-14\\-2x-6+\frac{18}{5}x=-14\\\frac{8}{5}x=-8 \\x=-5[/tex]
Replace the value of x into any of the two equations:
[tex]6(-5)+5y=10\\-30+5y=10\\5y=40\\y=8[/tex]
The values are x=-5 and y=8.
