Solve the system: x + 2y = 7 and 3x - y = -1. The solution is

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Prepare for the 8th Grade FAST Mathematics Test with our Pre-Algebra quiz. Study with multiple choice questions, each with hints and explanations. Build your confidence and ensure you're ready to excel!

Multiple Choice

Solve the system: x + 2y = 7 and 3x - y = -1. The solution is

Explanation:
Solving a system of linear equations often uses substitution: solve one equation for one variable and plug that expression into the other. From the second equation, y = 3x + 1. Put that into the first equation: x + 2(3x + 1) = 7 x + 6x + 2 = 7 7x + 2 = 7 7x = 5 x = 5/7 Now find y: y = 3x + 1 = 3(5/7) + 1 = 15/7 + 7/7 = 22/7 Check quickly: x + 2y = 5/7 + 44/7 = 49/7 = 7 3x − y = 15/7 − 22/7 = −7/7 = −1 So the solution is x = 5/7 and y = 22/7.

Solving a system of linear equations often uses substitution: solve one equation for one variable and plug that expression into the other.

From the second equation, y = 3x + 1.

Put that into the first equation:

x + 2(3x + 1) = 7

x + 6x + 2 = 7

7x + 2 = 7

7x = 5

x = 5/7

Now find y:

y = 3x + 1 = 3(5/7) + 1 = 15/7 + 7/7 = 22/7

Check quickly:

x + 2y = 5/7 + 44/7 = 49/7 = 7

3x − y = 15/7 − 22/7 = −7/7 = −1

So the solution is x = 5/7 and y = 22/7.

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