Solving Equations Using Substitution Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Solve the system of equations.
x=6y−3

2x+7y=13
(1 point)
(
,
)
R

Answer 1

To solve the system of equations using substitution, we can follow these steps:

1. We have the equations: \[ x = 6y - 3 \quad \text{(1)} \] \[ 2x + 7y = 13 \quad \text{(2)} \]

2. Substitute equation (1) into equation (2) for \(x\): \[ 2(6y - 3) + 7y = 13 \]

3. Distribute the 2: \[ 12y - 6 + 7y = 13 \]

4. Combine like terms: \[ 19y - 6 = 13 \]

5. Add 6 to both sides: \[ 19y = 19 \]

6. Divide by 19: \[ y = 1 \]

7. Now substitute \(y = 1\) back into equation (1) to find \(x\): \[ x = 6(1) - 3 \] \[ x = 6 - 3 \] \[ x = 3 \]

8. The solution to the system of equations is: \[ (x, y) = (3, 1) \]

Thus, the final answer is: \[ (3, 1) \]