QuestionJuly 15, 2025

Use the elimination method to solve the system of equations. 3x+2y=16 2x-2y=4 A. (2,4) B. (4,2) C. (5,3) D (4,14)

Use the elimination method to solve the system of equations. 3x+2y=16 2x-2y=4 A. (2,4) B. (4,2) C. (5,3) D (4,14)
Use the elimination method to solve the system of equations.
3x+2y=16
2x-2y=4
A. (2,4)
B. (4,2)
C. (5,3)
D (4,14)

Solution
4.4(332 votes)

Answer

B. (4,2) Explanation 1. Add the equations Add 3x + 2y = 16 and 2x - 2y = 4 to eliminate y: \[ (3x + 2y) + (2x - 2y) = 16 + 4 \] \[ 5x = 20 \] 2. Solve for x Divide both sides by 5: \[ x = \frac{20}{5} = 4 \] 3. Substitute x into one equation Use 3x + 2y = 16 with x = 4: \[ 3(4) + 2y = 16 \] \[ 12 + 2y = 16 \] 4. Solve for y Subtract 12 from both sides: \[ 2y = 4 \] Divide by 2: \[ y = \frac{4}{2} = 2 \]

Explanation

1. Add the equations<br /> Add $3x + 2y = 16$ and $2x - 2y = 4$ to eliminate $y$: <br />\[ (3x + 2y) + (2x - 2y) = 16 + 4 \]<br />\[ 5x = 20 \]<br /><br />2. Solve for $x$<br /> Divide both sides by 5:<br />\[ x = \frac{20}{5} = 4 \]<br /><br />3. Substitute $x$ into one equation<br /> Use $3x + 2y = 16$ with $x = 4$:<br />\[ 3(4) + 2y = 16 \]<br />\[ 12 + 2y = 16 \]<br /><br />4. Solve for $y$<br /> Subtract 12 from both sides:<br />\[ 2y = 4 \]<br /> Divide by 2:<br />\[ y = \frac{4}{2} = 2 \]
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