Question

Is (2, 6) a solution to this system of equations?

y = 3/2x + 3
y = -9x + 1
yes
no

Answer 1

To determine if (2, 6) is a solution to the system of equations:

y = 3/2x + 3 ... (equation 1)

y = -9x + 1 ... (equation 2)

We need to substitute x = 2 and y = 6 into both equations and check if they are true.

Substituting x = 2 and y = 6 into equation 1, we get:

6 = 3/2(2) + 3

6 = 3 + 3

6 = 6

This equation is true.

Substituting x = 2 and y = 6 into equation 2, we get:

6 = -9(2) + 1

6 = -18 + 1

6 = -17

This equation is false.

Since (2, 6) does not satisfy equation 2, it is not a solution to the system of equations. Therefore, the answer is: no.

Answer 2

To check if (2, 6) is a solution to the system of equations, we can substitute x=2 and y=6 into both equations and see if the left-hand sides equal the right-hand sides:

For the first equation: y = 3/2x + 3, substituting x=2 and y=6 gives:

6 = 3/2(2) + 3
6 = 3 + 3
6 = 6

This equation is true, so (2, 6) satisfies the first equation.

For the second equation: y = -9x + 1, substituting x=2 and y=6 gives:

6 = -9(2) + 1
6 = -18 + 1
6 = -17

This equation is not true, so (2, 6) does not satisfy the second equation.

Since (2, 6) does not satisfy both equations, it is not a solution to the system of equations. Therefore, the answer is "no".