Question

6x + 5y = 10, -2x -3y = -14

Solve the system of linear equations using any method.

Answer 1

(-5, 8)

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:

`6x+5y=10\\5y=10-6x\\y=2-(6)/(5)x`

Replace the isolated variable into the other equation:

`-2x-3(2-(6)/(5)x)=-14\\-2x-6+(18)/(5)x=-14\\(8)/(5)x=-8 \\x=-5`

Replace the value of x into any of the two equations:

`6(-5)+5y=10\\-30+5y=10\\5y=40\\y=8`

The values are x=-5 and y=8.