Is (4,9) a solution to this system of equations?

Question

y=3x–2
x=4

Answer 1

To determine if (4, 9) is a solution to the given system of equations, we need to check if this point satisfies both equations.

1. The first equation is \( y = 3x - 2 \). Substitute \( x = 4 \): \[ y = 3(4) - 2 = 12 - 2 = 10 \] So, when \( x = 4 \), \( y \) should be 10. Thus, the point that corresponds to \( x = 4 \) is (4, 10).

2. The second equation is \( x = 4 \), which simply indicates that \( x \) must be 4.

Now we can compare the \( y \)-value of the point (4, 9) with the calculated \( y \)-value when \( x = 4 \). Since we found that \( y \) should be 10, but (4, 9) has \( y = 9 \), (4, 9) does not satisfy the first equation.

Therefore, (4, 9) is not a solution to the system of equations.