Given the equations: x + 2y = 10 and 3x - y = 5, what is the value of y?

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Question: Given the equations: x + 2y = 10 and 3x - y = 5, what is the value of y?

Options:

Correct Answer: 2

Solution:

From the first equation, y = (10 - x)/2. Substituting into the second gives 3x - (10 - x)/2 = 5. Solving leads to y = 2.

Given the equations: x + 2y = 10 and 3x - y = 5, what is the value of y?

Given the equations: x + 2y = 10 and 3x - y = 5, what is the value of y?

Step 1: Start with the first equation: x + 2y = 10.
Step 2: Rearrange the first equation to solve for y: y = (10 - x) / 2.
Step 3: Now take the second equation: 3x - y = 5.
Step 4: Substitute the expression for y from Step 2 into the second equation: 3x - (10 - x) / 2 = 5.
Step 5: To eliminate the fraction, multiply the entire equation by 2: 2 * (3x) - (10 - x) = 10.
Step 6: This simplifies to 6x - 10 + x = 10.
Step 7: Combine like terms: 7x - 10 = 10.
Step 8: Add 10 to both sides: 7x = 20.
Step 9: Divide both sides by 7 to find x: x = 20 / 7.
Step 10: Now substitute x back into the equation for y: y = (10 - (20 / 7)) / 2.
Step 11: Simplify the expression for y: y = (70/7 - 20/7) / 2 = (50/7) / 2 = 25/7.
Step 12: Therefore, the value of y is 25/7.

Systems of Equations – The question tests the ability to solve a system of linear equations using substitution.
Algebraic Manipulation – The question requires skills in rearranging equations and substituting variables.