Question

For each ordered pair, determine whether it is a solution to the system of equations.
18x-3y=15
y=6x-5
(x, y)
Is it a solution?
Yes
No
(3,8)


(0, - 6)


(-1, - 11)


(2, 7)

Answer 1

To determine whether each ordered pair is a solution to the given system of equations, we can substitute the values of \(x\) and \(y\) from each pair into both equations and see if both equations are satisfied.

The system of equations is:
1. \(18x - 3y = 15\)
2. \(y = 6x - 5\)

### Checking (3, 8):
1. For the first equation:
\[ 18(3) - 3(8) = 54 - 24 = 30 \neq 15 \]
So it does not satisfy the first equation.

2. For the second equation:
\[ 8 = 6(3) - 5 = 18 - 5 = 13 \neq 8 \]
So it does not satisfy the second equation.

**Conclusion:** Not a solution.

### Checking (0, -6):
1. For the first equation:
\[ 18(0) - 3(-6) = 0 + 18 = 18 \neq 15 \]

2. For the second equation:
\[ -6 = 6(0) - 5 = 0 - 5 = -5 \neq -6 \]

**Conclusion:** Not a solution.

### Checking (-1, -11):
1. For the first equation:
\[ 18(-1) - 3(-11) = -18 + 33 = 15 \]
So it satisfies the first equation.

2. For the second equation:
\[ -11 = 6(-1) - 5 = -6 - 5 = -11 \]
So it satisfies the second equation.

**Conclusion:** Is a solution.

### Checking (2, 7):
1. For the first equation:
\[ 18(2) - 3(7) = 36 - 21 = 15 \]
So it satisfies the first equation.

2. For the second equation:
\[ 7 = 6(2) - 5 = 12 - 5 = 7 \]
So it satisfies the second equation.

**Conclusion:** Is a solution.

### Summary of Results:
- (3, 8): No
- (0, -6): No
- (-1, -11): Yes
- (2, 7): Yes