Solving Simultaneous Equations Using Substitution Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items

Question
Use the substitution method to solve the system 2x+2y=6
, 3x+2y=9
.(1 point)
(
)

Answer 1

To solve the system of equations using the substitution method, we have the following equations:

1. \( 2x + 2y = 6 \) (Equation 1)
2. \( 3x + 2y = 9 \) (Equation 2)

Step 1: Solve one of the equations for one variable. Let’s solve Equation 1 for \( y \).

Starting with Equation 1: \[ 2x + 2y = 6 \]

Subtract \( 2x \) from both sides: \[ 2y = 6 - 2x \]

Now, divide by 2: \[ y = 3 - x \quad \text{(Equation 3)} \]

Step 2: Substitute Equation 3 into Equation 2.

Now substitute \( y = 3 - x \) into Equation 2: \[ 3x + 2(3 - x) = 9 \]

Distributing \( 2 \): \[ 3x + 6 - 2x = 9 \]

Combine like terms: \[ x + 6 = 9 \]

Subtract \( 6 \) from both sides: \[ x = 3 \]

Step 3: Substitute \( x \) back into Equation 3 to find \( y \).

Now substitute \( x = 3 \) into Equation 3: \[ y = 3 - 3 \] \[ y = 0 \]

So the solution to the system of equations is: \[ (x, y) = (3, 0) \]

Thus, the answer is \( (3, 0) \).