Question

Solve the equation using elimination
3x+2y=12
-x+y=11

Answer 1

To solve the equation using elimination, we need to eliminate one of the variables by manipulating the equations.

- Start by multiplying the second equation by 3 to have the same coefficient for x as the first equation:
3(-x+y) = 3(11)
-3x + 3y = 33

- Next, add the two equations together to eliminate x:
(3x + 2y) + (-3x + 3y) = 12 + 33
5y = 45

- Divide both sides of the equation by 5 to solve for y:
5y/5 = 45/5
y = 9

- Substitute the value of y (9) into the second equation to solve for x:
-x + 9 = 11
-x = 2

- Multiply both sides of the equation by -1 to solve for x:
(-1)(-x) = 2(-1)
x = -2

Therefore, the solution to the equation is x = -2 and y = 9.