If 5x + 3y = 30 and 2x + y = 12, what is the value of y?

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Question: If 5x + 3y = 30 and 2x + y = 12, what is the value of y?

Options:

Correct Answer: 5

Solution:

From the second equation, y = 12 - 2x. Substituting into the first gives 5x + 3(12 - 2x) = 30. Solving gives y = 5.

If 5x + 3y = 30 and 2x + y = 12, what is the value of y?

If 5x + 3y = 30 and 2x + y = 12, what is the value of y?

Step 1: Start with the two equations: 5x + 3y = 30 and 2x + y = 12.
Step 2: From the second equation (2x + y = 12), isolate y by subtracting 2x from both sides: y = 12 - 2x.
Step 3: Now, substitute the expression for y (12 - 2x) into the first equation (5x + 3y = 30).
Step 4: Replace y in the first equation: 5x + 3(12 - 2x) = 30.
Step 5: Distribute 3 in the equation: 5x + 36 - 6x = 30.
Step 6: Combine like terms (5x - 6x): -x + 36 = 30.
Step 7: Subtract 36 from both sides: -x = 30 - 36, which simplifies to -x = -6.
Step 8: Multiply both sides by -1 to solve for x: x = 6.
Step 9: Now that we have x, substitute x back into the equation for y: y = 12 - 2(6).
Step 10: Calculate y: y = 12 - 12, which gives y = 0.

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