Answer :
To determine if the point [tex]\((-4, 2)\)[/tex] is a solution to the system of equations:
[tex]\[ \begin{array}{l} y = -\frac{1}{4}x + 1 \\ y = \frac{1}{2}x - 1 \end{array} \][/tex]
we need to check if the point satisfies both of these equations.
Step 1: Check the first equation
Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 2\)[/tex] into the first equation:
[tex]\[ y = -\frac{1}{4}x + 1 \][/tex]
[tex]\[ 2 = -\frac{1}{4}(-4) + 1 \][/tex]
Calculate the right-hand side:
[tex]\[ 2 = 1 + 1 \][/tex]
[tex]\[ 2 = 2 \][/tex]
The point [tex]\((-4, 2)\)[/tex] satisfies the first equation.
Step 2: Check the second equation
Now, substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 2\)[/tex] into the second equation:
[tex]\[ y = \frac{1}{2}x - 1 \][/tex]
[tex]\[ 2 = \frac{1}{2}(-4) - 1 \][/tex]
Calculate the right-hand side:
[tex]\[ 2 = -2 - 1 \][/tex]
[tex]\[ 2 = -3 \][/tex]
The point [tex]\((-4, 2)\)[/tex] does not satisfy the second equation.
Conclusion:
The point [tex]\((-4, 2)\)[/tex] satisfies the first equation but does not satisfy the second equation. Since a solution to the system of equations must satisfy both equations simultaneously, the point [tex]\((-4, 2)\)[/tex] is not a solution to the system of equations.
Therefore, the answer is no.
[tex]\[ \begin{array}{l} y = -\frac{1}{4}x + 1 \\ y = \frac{1}{2}x - 1 \end{array} \][/tex]
we need to check if the point satisfies both of these equations.
Step 1: Check the first equation
Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 2\)[/tex] into the first equation:
[tex]\[ y = -\frac{1}{4}x + 1 \][/tex]
[tex]\[ 2 = -\frac{1}{4}(-4) + 1 \][/tex]
Calculate the right-hand side:
[tex]\[ 2 = 1 + 1 \][/tex]
[tex]\[ 2 = 2 \][/tex]
The point [tex]\((-4, 2)\)[/tex] satisfies the first equation.
Step 2: Check the second equation
Now, substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 2\)[/tex] into the second equation:
[tex]\[ y = \frac{1}{2}x - 1 \][/tex]
[tex]\[ 2 = \frac{1}{2}(-4) - 1 \][/tex]
Calculate the right-hand side:
[tex]\[ 2 = -2 - 1 \][/tex]
[tex]\[ 2 = -3 \][/tex]
The point [tex]\((-4, 2)\)[/tex] does not satisfy the second equation.
Conclusion:
The point [tex]\((-4, 2)\)[/tex] satisfies the first equation but does not satisfy the second equation. Since a solution to the system of equations must satisfy both equations simultaneously, the point [tex]\((-4, 2)\)[/tex] is not a solution to the system of equations.
Therefore, the answer is no.
