To solve the system of equations using substitution, we need to follow these steps:
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Identify the equations:
We have the following two equations: \[- \quad y = x - 5 \quad \text{(Equation 1)} \] \[
- \quad 4x + 2y = 14 \quad \text{(Equation 2)} \]
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Substitute \(y\) from Equation 1 into Equation 2:
Since Equation 1 gives us \(y\) in terms of \(x\), we can substitute this expression for \(y\) into Equation 2.Replacing \(y\) in Equation 2: \[ 4x + 2(x - 5) = 14 \]
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Simplify the equation:
Distribute the 2: \[ 4x + 2x - 10 = 14 \] Combine like terms: \[ 6x - 10 = 14 \] -
Solve for \(x\):
First, add 10 to both sides: \[ 6x = 14 + 10 \] \[ 6x = 24 \] Now, divide by 6: \[ x = \frac{24}{6} = 4 \] -
Substitute \(x\) back into Equation 1 to find \(y\):
Now that we have \(x = 4\), we can find \(y\) using Equation 1: \[ y = x - 5 \] \[ y = 4 - 5 = -1 \] -
Final Solution:
The solution to the system of equations is: \[ (x, y) = (4, -1) \] -
Verification:
We can verify our solution by substituting \(x = 4\) and \(y = -1\) back into the second equation: \[ 4(4) + 2(-1) = 16 - 2 = 14 \] This is correct, thus confirming our solution is valid.
Therefore, the final answer is: \[ \boxed{(4, -1)} \]