Solve using elimination.

2x − 5y = -6
-3x + 5y = 14

To solve the given system of equations using elimination, we'll add the two equations together to eliminate the y term.

Step 1: Add the equations
(2x - 5y) + (-3x + 5y) = -6 + 14

This simplifies to:
2x - 5y - 3x + 5y = 8

Step 2: Combine like terms
(2x - 3x) + (-5y + 5y) = 8

This simplifies to:
-x = 8

Step 3: Solve for x
Multiply both sides of the equation by -1:
(-1)(-x) = (-1)(8)
x = -8

Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using the first equation,
2(-8) - 5y = -6

Simplify:
-16 - 5y = -6

Step 5: Solve for y
Add 16 to both sides of the equation:
-5y = 10

Divide both sides by -5:
y = -2

So, the solution to the given system of equations is x = -8 and y = -2.

add the two equations

-x + 0y=8
x=-8
to elimate x, multiply the first equation by 1.5
3x-7.5y=-9 then add
-3x+5y=14
to get -2.5y=5
y=-2