To solve the system of equations using substitution, we'll follow these steps:
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Write down the two equations: \[ y = 2x + 4 \quad \text{(1)} \] \[ 3x + 2y = 22 \quad \text{(2)} \]
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Substitute equation (1) into equation (2). Since \( y \) is expressed in terms of \( x \) in equation (1), we can replace \( y \) in equation (2) with \( 2x + 4 \): \[ 3x + 2(2x + 4) = 22 \]
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Now, simplify the equation: \[ 3x + 4x + 8 = 22 \]
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Combine the like terms: \[ 7x + 8 = 22 \]
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Now, isolate \( x \) by subtracting 8 from both sides: \[ 7x = 22 - 8 \] \[ 7x = 14 \]
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Divide both sides by 7: \[ x = 2 \]
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Now that we have the value of \( x \), we can find \( y \) using equation (1): \[ y = 2(2) + 4 \] \[ y = 4 + 4 \] \[ y = 8 \]
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Thus, the solution to the system of equations is: \[ (x, y) = (2, 8) \]
Final Answer: \[ x = 2, \quad y = 8 \]