To solve the system of equations using substitution, we'll start with the two equations given:
- \( 2x + y = -14 \)
- \( 10x - 4y = 2 \)
First, we can solve the first equation for \( y \):
\[ y = -14 - 2x \]
Next, we will substitute this expression for \( y \) into the second equation.
Substituting \( y \) in equation 2:
\[ 10x - 4(-14 - 2x) = 2 \]
Now, we will simplify this equation:
\[ 10x + 56 + 8x = 2 \]
Combine like terms:
\[ 18x + 56 = 2 \]
Next, isolate \( x \) by subtracting 56 from both sides:
\[ 18x = 2 - 56 \] \[ 18x = -54 \]
Now, divide by 18:
\[ x = \frac{-54}{18} = -3 \]
Now that we have \( x \), we can substitute it back into the equation for \( y \):
\[ y = -14 - 2(-3) \] \[ y = -14 + 6 \] \[ y = -8 \]
We have found \( x \) and \( y \):
\[ x = -3, \quad y = -8 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-3, -8) \]
To verify, let's plug \( x \) and \( y \) back into both original equations:
- \( 2(-3) + (-8) = -6 - 8 = -14 \) (True)
- \( 10(-3) - 4(-8) = -30 + 32 = 2 \) (True)
Both equations are satisfied, confirming our solution is correct. The final solution is:
\[ \boxed{(-3, -8)} \]
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