Question

Is (3,9) a solution to this system of equations?
y=5x+9

y=x+6

Answer 1

No

Explanation:

y=5x+9

y=x+6

`y = 5x + 9 \: \: - - - - - - (1) \\ y = x + 6 \: \: - - - - - - -(2) \\ from \: equation \: (2) \\ y - 6 = x \\ x = 6 + y - - - - - - (3)\\ y = 5x + 9 \\ y = 5(6 + y) + 9 \\ y = 30 + 5y + 9 \\ 5y - y = 30 + 9 \\ 4y = 39 \\ y = - (39)/(4) \\ y = 9.75 \\ \\ y = 9.75 \: into \: (2) \\y = x + 6 \\ 9.75 = x + 6 \\ 9.75 - 6 = x \\ x = 9.75 - 6 \\ x = 3.75`

So the answer is NO

Answer 2

No

Explanation:

substitute the x- coordinate of the point into each equation and if both have the value of the y- coordinate of the point then it is a solution.

y = 5(3) + 9 = 15 + 9 = 24 ≠ 9

y = 3 + 6 = 9

since the point does not satisfy both equations then it is not a solution of the system.