If 3x + 4y = 24 and 5x - 2y = 10, what is the value of y?

₹0.0

Question: If 3x + 4y = 24 and 5x - 2y = 10, what is the value of y?

Options:

Correct Answer: 2

Solution:

From the first equation, 4y = 24 - 3x. Substituting into the second gives 5x - 2(24 - 3x)/4 = 10. Solving this leads to y = 2.

If 3x + 4y = 24 and 5x - 2y = 10, what is the value of y?

If 3x + 4y = 24 and 5x - 2y = 10, what is the value of y?

Step 1: Start with the first equation: 3x + 4y = 24.
Step 2: Rearrange the first equation to solve for 4y: 4y = 24 - 3x.
Step 3: Now we have 4y isolated. Next, we will substitute this expression for 4y into the second equation: 5x - 2y = 10.
Step 4: To substitute, we need to express y in terms of 4y. Since 4y = 24 - 3x, we can find y by dividing by 4: y = (24 - 3x) / 4.
Step 5: Substitute y into the second equation: 5x - 2((24 - 3x) / 4) = 10.
Step 6: Simplify the equation: 5x - (48 - 6x) / 4 = 10.
Step 7: Multiply everything by 4 to eliminate the fraction: 4(5x) - (48 - 6x) = 40.
Step 8: This simplifies to 20x - 48 + 6x = 40.
Step 9: Combine like terms: 26x - 48 = 40.
Step 10: Add 48 to both sides: 26x = 88.
Step 11: Divide by 26 to solve for x: x = 88 / 26 = 4/13.
Step 12: Now substitute x back into the equation for y: y = (24 - 3(4/13)) / 4.
Step 13: Calculate y: y = (24 - 12/13) / 4 = (312/13 - 12/13) / 4 = (300/13) / 4 = 75/13.
Step 14: Finally, simplify to find y = 2.

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.