Solve the linear system: 2x + 3y = 12 and x - y = 2. Find x and y.

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Multiple Choice

Solve the linear system: 2x + 3y = 12 and x - y = 2. Find x and y.

Explanation:
Solving a pair of linear equations by substitution means express one variable from one equation and substitute that expression into the other equation to eliminate the other variable. From the equation x − y = 2, we get x = y + 2. Plug that into 2x + 3y = 12: 2(y + 2) + 3y = 12 simplifies to 2y + 4 + 3y = 12, so 5y + 4 = 12, giving y = 8/5. Then x = y + 2 = 8/5 + 2 = 18/5. Checking: 2x + 3y = 2*(18/5) + 3*(8/5) = 36/5 + 24/5 = 60/5 = 12, and x − y = 18/5 − 8/5 = 10/5 = 2. The solution is x = 18/5, y = 8/5.

Solving a pair of linear equations by substitution means express one variable from one equation and substitute that expression into the other equation to eliminate the other variable. From the equation x − y = 2, we get x = y + 2. Plug that into 2x + 3y = 12: 2(y + 2) + 3y = 12 simplifies to 2y + 4 + 3y = 12, so 5y + 4 = 12, giving y = 8/5. Then x = y + 2 = 8/5 + 2 = 18/5. Checking: 2x + 3y = 2*(18/5) + 3*(8/5) = 36/5 + 24/5 = 60/5 = 12, and x − y = 18/5 − 8/5 = 10/5 = 2. The solution is x = 18/5, y = 8/5.

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