Math  /  Algebra

Question竣 Is (3,9)(3,9) a solution to this system of equations? y=5x+9y=x+6\begin{array}{l} y=5 x+9 \\ y=x+6 \end{array} yes no

Studdy Solution

STEP 1

1. We have a system of two linear equations.
2. We need to check if the point (3,9)(3,9) satisfies both equations simultaneously.

STEP 2

1. Substitute the point (3,9)(3,9) into the first equation and check if it holds true.
2. Substitute the point (3,9)(3,9) into the second equation and check if it holds true.
3. Determine if (3,9)(3,9) is a solution to the system based on the results of the substitutions.

STEP 3

Substitute x=3 x = 3 and y=9 y = 9 into the first equation y=5x+9 y = 5x + 9 :
9=5(3)+9 9 = 5(3) + 9 9=15+9 9 = 15 + 9 9=24 9 = 24
The equation does not hold true.

STEP 4

Substitute x=3 x = 3 and y=9 y = 9 into the second equation y=x+6 y = x + 6 :
9=3+6 9 = 3 + 6 9=9 9 = 9
The equation holds true.

STEP 5

Since the point (3,9)(3,9) does not satisfy the first equation, it is not a solution to the system of equations.
The answer is no\boxed{\text{no}}.

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