Solve the system: x + y = 7, 2x - y = 1. What are x and y?

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Multiple Choice

Solve the system: x + y = 7, 2x - y = 1. What are x and y?

Explanation:
When solving a pair of linear equations, you can add the equations to eliminate a variable. Here, adding x + y = 7 and 2x − y = 1 cancels the y terms: (x + y) + (2x − y) = 7 + 1, which gives 3x = 8, so x = 8/3. Now substitute x = 8/3 into x + y = 7: 8/3 + y = 7, so y = 7 − 8/3 = 13/3. Check with the second equation: 2x − y = 2*(8/3) − 13/3 = 16/3 − 13/3 = 3/3 = 1, which holds. The solution is x = 8/3 and y = 13/3.

When solving a pair of linear equations, you can add the equations to eliminate a variable. Here, adding x + y = 7 and 2x − y = 1 cancels the y terms: (x + y) + (2x − y) = 7 + 1, which gives 3x = 8, so x = 8/3. Now substitute x = 8/3 into x + y = 7: 8/3 + y = 7, so y = 7 − 8/3 = 13/3. Check with the second equation: 2x − y = 2*(8/3) − 13/3 = 16/3 − 13/3 = 3/3 = 1, which holds. The solution is x = 8/3 and y = 13/3.

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