Question

the point $(-1, 5)$ is the solution to a set of linear equations. one of the equations is $y = -2x + 3$. which of the following cannot be the other equation?

a. $y = -x + 4$

b. $y = -2x$

c. $y = -5x$

d. $y = -\frac{1}{2}x + \frac{9}{2}$

Explanation:

Step1: Recall solution of linear equations

A solution to a set of linear equations satisfies all equations. So, substitute \( x = -1 \) and \( y = 5 \) into each option to check.

Step2: Check Option A

Substitute \( x=-1 \), \( y = 5 \) into \( y=-x + 4 \):
Right - hand side (RHS): \( -(-1)+4=1 + 4=5 \), which equals left - hand side (LHS) \( y = 5 \). So, \((-1,5)\) is a solution for this equation.

Step3: Check Option B

Substitute \( x=-1 \), \( y = 5 \) into \( y=-2x \):
RHS: \( -2\times(-1)=2
eq5 \). So, \((-1,5)\) is not a solution for this equation.

Step4: Check Option C

Substitute \( x=-1 \), \( y = 5 \) into \( y=-5x \):
RHS: \( -5\times(-1)=5 \), which equals LHS \( y = 5 \). So, \((-1,5)\) is a solution for this equation.

Step5: Check Option D

Substitute \( x=-1 \), \( y = 5 \) into \( y=-\frac{1}{2}x+\frac{9}{2}\):
RHS: \( -\frac{1}{2}\times(-1)+\frac{9}{2}=\frac{1}{2}+\frac{9}{2}=\frac{1 + 9}{2}=5 \), which equals LHS \( y = 5 \). So, \((-1,5)\) is a solution for this equation.

Answer:

B. \( y=-2x \)