To solve the system of equations using substitution, we will use the first equation to substitute for \(y\) in the second equation.
We are given:
- \( y = 4x + 10 \) (Equation 1)
- \( y = 3x + 6 \) (Equation 2)
Since both equations are equal to \(y\), we can set them equal to each other:
\[ 4x + 10 = 3x + 6 \]
Now, we solve for \(x\):
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Subtract \(3x\) from both sides: \[ 4x - 3x + 10 = 6 \] This simplifies to: \[ x + 10 = 6 \]
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Subtract \(10\) from both sides: \[ x = 6 - 10 \] This simplifies to: \[ x = -4 \]
Now that we have \(x\), we will substitute \(x = -4\) back into either original equation to find \(y\). We'll use Equation 1:
\[ y = 4(-4) + 10 \] This simplifies to: \[ y = -16 + 10 \] \[ y = -6 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, -6) \]
To verify, we can substitute \(x = -4\) into Equation 2:
\[ y = 3(-4) + 6 \] This simplifies to: \[ y = -12 + 6 \] \[ y = -6 \]
Both equations give the same \(y\) value. Therefore, the solution is confirmed:
\[ \boxed{(-4, -6)} \]