Question
*. Algebra The solution to the linear system \( x=-3, y=m x-\frac{7}{2} \) is \( (-3,1) \). What is the value of \( m \) ?
Ask by Crawford Guzman. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of \( m \) is \(-\frac{3}{2}\).
Solution
1. Substitute \( x = -3 \) into the equation for \( y \):
\[
y = m(-3) - \frac{7}{2}
\]
2. Since the solution is given as \( (-3, 1) \), we know \( y = 1 \). Therefore, set:
\[
1 = -3m - \frac{7}{2}
\]
3. Add \(\frac{7}{2}\) to both sides:
\[
1 + \frac{7}{2} = -3m
\]
Convert \(1\) to a fraction with denominator 2:
\[
\frac{2}{2} + \frac{7}{2} = \frac{9}{2} = -3m
\]
4. Solve for \( m \) by dividing both sides by \(-3\):
\[
m = -\frac{\frac{9}{2}}{3} = -\frac{9}{6} = -\frac{3}{2}
\]
Thus, the value of \( m \) is \(-\frac{3}{2}\).
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Simplify this solution The Deep Dive
To find the value of \( m \), we substitute \( x = -3 \) into the equation \( y = m x - \frac{7}{2} \). Since we know that the solution is \( (-3, 1) \), we can set \( y = 1 \). Thus, the equation becomes: \[ 1 = m(-3) - \frac{7}{2} \] Rearranging gives: \[ 1 + \frac{7}{2} = -3m \] Converting \( 1 \) to a fraction gives \( \frac{2}{2} \), so: \[ \frac{2}{2} + \frac{7}{2} = -3m \] This simplifies to: \[ \frac{9}{2} = -3m \] Dividing both sides by -3 leads to: \[ m = -\frac{3}{9} = -\frac{1}{3} \] Thus, the value of \( m \) is \( -\frac{1}{3} \).
