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

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

Options:

Correct Answer: 4

Solution:

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

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

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

Step 1: Start with the two equations: 5x + 3y = 30 and 2x + y = 12.
Step 2: Solve the second equation for y. Rearranging gives y = 12 - 2x.
Step 3: Substitute the expression for y from Step 2 into the first equation. This means replacing y in 5x + 3y = 30 with (12 - 2x).
Step 4: The equation now looks like this: 5x + 3(12 - 2x) = 30.
Step 5: Distribute the 3 in the equation: 5x + 36 - 6x = 30.
Step 6: Combine like terms: (5x - 6x) + 36 = 30, which simplifies to -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.

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.