Solve the system: x + 2y = 10 and 3x - y = 5

Prepare for the TSI A2 Mathematics Test. Enhance your skills with comprehensive questions, detailed solutions, and effective strategies. Succeed on your exam!

Multiple Choice

Solve the system: x + 2y = 10 and 3x - y = 5

Explanation:
Solving a system of two linear equations often uses substitution to find the exact values that satisfy both. From the first equation, express x in terms of y: x = 10 − 2y. Substitute this into the second equation: 3(10 − 2y) − y = 5. This becomes 30 − 6y − y = 5, so 30 − 7y = 5. Subtract 30: −7y = −25, giving y = 25/7. Now plug y back into x = 10 − 2y: x = 10 − 2(25/7) = 10 − 50/7 = 70/7 − 50/7 = 20/7. Check: x + 2y = 20/7 + 50/7 = 70/7 = 10, and 3x − y = 60/7 − 25/7 = 35/7 = 5. Both true, so the solution is x = 20/7 and y = 25/7.

Solving a system of two linear equations often uses substitution to find the exact values that satisfy both.

From the first equation, express x in terms of y: x = 10 − 2y. Substitute this into the second equation: 3(10 − 2y) − y = 5. This becomes 30 − 6y − y = 5, so 30 − 7y = 5. Subtract 30: −7y = −25, giving y = 25/7. Now plug y back into x = 10 − 2y: x = 10 − 2(25/7) = 10 − 50/7 = 70/7 − 50/7 = 20/7.

Check: x + 2y = 20/7 + 50/7 = 70/7 = 10, and 3x − y = 60/7 − 25/7 = 35/7 = 5. Both true, so the solution is x = 20/7 and y = 25/7.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy