Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What

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Question: Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What is the value of y?

Options:

Correct Answer: 3

Solution:

From the second equation, y = 2x - 3. Substituting into the first gives 4x + 5(2x - 3) = 20. Solving leads to y = 3.

Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What is the value of y?

Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What is the value of y?

Step 1: Start with the two equations: 4x + 5y = 20 and 2x - y = 3.
Step 2: Rearrange the second equation (2x - y = 3) to solve for y. This gives us y = 2x - 3.
Step 3: Substitute the expression for y (from Step 2) into the first equation (4x + 5y = 20).
Step 4: Replace y in the first equation with (2x - 3): 4x + 5(2x - 3) = 20.
Step 5: Distribute 5 in the equation: 4x + 10x - 15 = 20.
Step 6: Combine like terms: 14x - 15 = 20.
Step 7: Add 15 to both sides of the equation: 14x = 35.
Step 8: Divide both sides by 14 to find x: x = 35 / 14 = 2.5.
Step 9: Now substitute x back into the equation for y (y = 2x - 3) to find y: y = 2(2.5) - 3.
Step 10: Calculate y: y = 5 - 3 = 2.

Simultaneous Equations – The question tests the ability to solve a system of linear equations using substitution.
Substitution Method – The solution involves substituting one variable in terms of another to simplify the equations.