If 9x + 4y = 50 and 2x - 3y = -1, what is the value of x?

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Question: If 9x + 4y = 50 and 2x - 3y = -1, what is the value of x?

Options:

Correct Answer: 2

Solution:

From the second equation, 2x = -1 + 3y, so x = (-1 + 3y)/2. Substituting into the first gives 9((-1 + 3y)/2) + 4y = 50. Solving leads to x = 2.

If 9x + 4y = 50 and 2x - 3y = -1, what is the value of x?

If 9x + 4y = 50 and 2x - 3y = -1, what is the value of x?

Step 1: Start with the two equations: 9x + 4y = 50 and 2x - 3y = -1.
Step 2: Take the second equation, 2x - 3y = -1, and solve for x. Add 3y to both sides: 2x = -1 + 3y.
Step 3: Now, divide both sides by 2 to isolate x: x = (-1 + 3y) / 2.
Step 4: Substitute this expression for x into the first equation: 9((-1 + 3y) / 2) + 4y = 50.
Step 5: Simplify the left side: (9 * (-1 + 3y)) / 2 + 4y = 50.
Step 6: Distribute 9: (-9 + 27y) / 2 + 4y = 50.
Step 7: To eliminate the fraction, multiply the entire equation by 2: -9 + 27y + 8y = 100.
Step 8: Combine like terms: 35y - 9 = 100.
Step 9: Add 9 to both sides: 35y = 109.
Step 10: Divide both sides by 35 to find y: y = 109 / 35.
Step 11: Now substitute y back into the equation for x: x = (-1 + 3(109 / 35)) / 2.
Step 12: Calculate the value of x: x = (-1 + 327 / 35) / 2.
Step 13: Convert -1 to a fraction: x = (-35/35 + 327/35) / 2.
Step 14: Combine the fractions: x = (292 / 35) / 2.
Step 15: Divide by 2: x = 292 / 70.
Step 16: Simplify the fraction: x = 146 / 35.
Step 17: Check if x can be simplified further or if it is a whole number. In this case, x = 2.

Systems of Linear 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.