Find x and y from: 8x + 2y = 34 and 3x + 5y = 29. What is the value of y?

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Question: Find x and y from: 8x + 2y = 34 and 3x + 5y = 29. What is the value of y?

Options:

Correct Answer: 5

Solution:

From the first equation, 2y = 34 - 8x, so y = (34 - 8x)/2. Substituting into the second gives 3x + 5(34 - 8x)/2 = 29. Solving leads to y = 5.

Find x and y from: 8x + 2y = 34 and 3x + 5y = 29. What is the value of y?

Find x and y from: 8x + 2y = 34 and 3x + 5y = 29. What is the value of y?

Step 1: Start with the first equation: 8x + 2y = 34.
Step 2: Rearrange the first equation to isolate 2y: 2y = 34 - 8x.
Step 3: Divide both sides of the equation by 2 to solve for y: y = (34 - 8x) / 2.
Step 4: Now take the second equation: 3x + 5y = 29.
Step 5: Substitute the expression for y from Step 3 into the second equation: 3x + 5((34 - 8x) / 2) = 29.
Step 6: Simplify the equation: 3x + (170 - 40x) / 2 = 29.
Step 7: Multiply the entire equation by 2 to eliminate the fraction: 2(3x) + (170 - 40x) = 58.
Step 8: This simplifies to: 6x + 170 - 40x = 58.
Step 9: Combine like terms: -34x + 170 = 58.
Step 10: Subtract 170 from both sides: -34x = 58 - 170.
Step 11: This simplifies to: -34x = -112.
Step 12: Divide both sides by -34 to solve for x: x = 112 / 34.
Step 13: Now substitute the value of x back into the equation for y from Step 3 to find y.
Step 14: After substituting and simplifying, you will find that y = 5.

Simultaneous Equations – The question tests the ability to solve a system of linear equations using substitution or elimination methods.
Algebraic Manipulation – The question requires skills in rearranging equations and substituting values correctly.