To solve the system of equations given:
- \( 2x - y = 10 \)
- \( y = -\frac{1}{2}x + 5 \)
We can use substitution or elimination. Here, we can substitute the second equation into the first equation.
From the second equation, we have:
\[ y = -\frac{1}{2}x + 5 \]
Now substitute this expression for \( y \) into the first equation:
\[ 2x - \left(-\frac{1}{2}x + 5\right) = 10 \]
Simplifying this gives:
\[ 2x + \frac{1}{2}x - 5 = 10 \]
Combining terms:
\[ 2x + \frac{1}{2}x = \frac{4}{2}x + \frac{1}{2}x = \frac{5}{2}x \]
So we have:
\[ \frac{5}{2}x - 5 = 10 \]
Now, add 5 to both sides:
\[ \frac{5}{2}x = 15 \]
Now, multiply both sides by \(\frac{2}{5}\):
\[ x = 15 \cdot \frac{2}{5} = 6 \]
Next, we substitute \( x = 6 \) back into the second equation to find \( y \):
\[ y = -\frac{1}{2}(6) + 5 \] \[ y = -3 + 5 = 2 \]
So, the solution to the system of equations is:
\[ (x, y) = (6, 2) \]
Therefore, the answer is \((6, 2)\).
1 answer