To solve the system of equations using the substitution method, let's first rewrite the equations clearly. The equations appear to be:
- \( 6 = -4x + y \)
- \(-5x - y = 21 \)
First, we can solve for \( y \) from the first equation:
\[ y = 6 + 4x \]
Next, we substitute this expression for \( y \) into the second equation:
\[ -5x - (6 + 4x) = 21 \]
Now, we simplify this equation:
\[ -5x - 6 - 4x = 21 \] \[ -9x - 6 = 21 \]
Next, we add 6 to both sides:
\[ -9x = 21 + 6 \] \[ -9x = 27 \]
Now, we divide by -9:
\[ x = -3 \]
With \( x \) found, we can substitute this value back into the equation for \( y \):
\[ y = 6 + 4(-3) \] \[ y = 6 - 12 \] \[ y = -6 \]
So, the solution to the system of equations is:
\[ (x, y) = (-3, -6) \]
Enter your answer as:
\((-3, -6)\)
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