What is the point of intersection of the lines x + 2y = 5 and 2x - y = 1?

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Question: What is the point of intersection of the lines x + 2y = 5 and 2x - y = 1?

Options:

Correct Answer: (1, 2)

Solution:

Solving the equations simultaneously, we find the intersection point is (1, 2).

What is the point of intersection of the lines x + 2y = 5 and 2x - y = 1?

What is the point of intersection of the lines x + 2y = 5 and 2x - y = 1?

Step 1: Write down the two equations: x + 2y = 5 and 2x - y = 1.
Step 2: Solve one of the equations for one variable. Let's solve the first equation for x: x = 5 - 2y.
Step 3: Substitute the expression for x from Step 2 into the second equation: 2(5 - 2y) - y = 1.
Step 4: Simplify the equation: 10 - 4y - y = 1, which becomes 10 - 5y = 1.
Step 5: Solve for y: 10 - 1 = 5y, so 9 = 5y, and y = 9/5 or y = 1.8.
Step 6: Now substitute y back into the expression for x: x = 5 - 2(1.8).
Step 7: Calculate x: x = 5 - 3.6, which gives x = 1.4.
Step 8: The point of intersection is (1.4, 1.8).

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