Question

Solve the system of equations using elimination. −3x + 2y = 9 x + y = 12 (−3, 0) (1, 6) (3, 9) (5, 7)

Answer 1

To solve the system of equations using elimination, we manipulated the equations to cancel out x, solving for y, and then substituted the value of y back into one equation to solve for x. The final solution to the system is (3, 9).

Step-by-step explanation:

To solve the system of equations using elimination, we must manipulate the equations to eliminate one of the variables. We have the system:

• -3x + 2y = 9
• x + y = 12

First, let's multiply the second equation by 3 to make the coefficient of x the same (but opposite in sign) as in the first equation.

• 3(x + y) = 3(12)
• 3x + 3y = 36

Now we have:

• -3x + 2y = 9
• 3x + 3y = 36

Adding these equations together, we get:

• (-3x + 3x) + (2y + 3y) = 9 + 36
• 0x + 5y = 45

Now, we can solve for y:

• 5y = 45
• y = 9

Substitute y = 9 into the second original equation to find x:

• x + 9 = 12
• x = 12 - 9
• x = 3

The solution to the system of equations is (x, y) = (3, 9).

Answer 2

(3, 9)

Step-by-step explanation:

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