Solve the following pair of equations: $7x+6y= 71$ $5x-8y= -23$
- $x= -5;y= 4$
- $x= 3,y= -2$
- $x= 5,y= 6$
- $x= 1,y= 3$
Reveal answer
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C
Correct answer
Explanation
Solving 7x + 6y = 71 and 5x - 8y = -23. Multiply first by 4 and second by 3: 28x + 24y = 284 and 15x - 24y = -69. Adding them gives 43x = 215, so x = 5. Substituting x=5 into the first equation: 35 + 6y = 71, 6y = 36, y = 6.
AI explanation
Using the elimination method, multiply the first equation by 4 to get 28x + 24y = 284, and multiply the second equation by 3 to get 15x - 24y = -69. Adding these two modified equations eliminates y and gives 43x = 215. Solving for x yields x = 5. Substituting x = 5 into the first equation, 7(5) + 6y = 71, gives 35 + 6y = 71, so 6y = 36 and y = 6.