Question

Solve each system using elimination or substitution. Show all work. Your final answer should be written as an ordered pair.

-2x + 3y = -13 and 3x - 3y = 12
A. (3, 2)
B. (-3, -4)
C. (2, 3)
D. (-2, -3)

Answer 1

To solve this system of equations using elimination, multiply the second equation by 2 to make the y-coefficients cancel out. Then solve for x and substitute the value into one of the original equations to find y.

Step-by-step explanation:

To solve this system of equations using elimination or substitution, we'll start by choosing a method.

Since the coefficients of the y-terms are opposites of each other, we'll use elimination.

We'll multiply the second equation by 2 to make the coefficients of y cancel out.

The new system of equations becomes:

-2x + 3y = -13

6x - 6y = 24

Adding the equations together, we get:

4x = 11

Solving for x, we find that x = 11/4. Substituting this value back into the first equation, we can solve for y:

-2(11/4) + 3y = -13

-11/2 + 3y = -13

3y = -13 + 11/2

3y = -15/2

y = (-15/2)/3

y = -5/2

So the solution to the system is the ordered pair (x, y) = (11/4, -5/2).