Math  /  Algebra

Question5. Given x=2y+3x=2 y+3 and 2x+y=112 x+y=11 would (5,1)(5,-1) be a solution to the system? Justify your answer.

Studdy Solution

STEP 1

1. We have a system of equations: x=2y+3 x = 2y + 3 and 2x+y=11 2x + y = 11 .
2. We need to verify if the point (5,1) (5, -1) satisfies both equations.

STEP 2

1. Substitute the point into the first equation and check if it holds true.
2. Substitute the point into the second equation and check if it holds true.
3. Conclude whether the point is a solution to the system.

STEP 3

Substitute x=5 x = 5 and y=1 y = -1 into the first equation x=2y+3 x = 2y + 3 .
5=2(1)+3 5 = 2(-1) + 3
Calculate the right side:
5=2+3 5 = -2 + 3
5=1 5 = 1
The equation does not hold true.

STEP 4

Substitute x=5 x = 5 and y=1 y = -1 into the second equation 2x+y=11 2x + y = 11 .
2(5)+(1)=11 2(5) + (-1) = 11
Calculate the left side:
101=9 10 - 1 = 9
The equation does not hold true.

STEP 5

Since the point (5,1) (5, -1) does not satisfy either of the equations, it is not a solution to the system.
The point (5,1) (5, -1) is not a solution to the system of equations.

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