What is the point of intersection of the lines y = 2x + 1 and y = -x + 4?

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Question: What is the point of intersection of the lines y = 2x + 1 and y = -x + 4?

Options:

Correct Answer: (1, 3)

Solution:

Setting 2x + 1 = -x + 4 gives 3x = 3, thus x = 1. Substituting back, y = 2(1) + 1 = 3. The intersection is (1, 3).

What is the point of intersection of the lines y = 2x + 1 and y = -x + 4?

What is the point of intersection of the lines y = 2x + 1 and y = -x + 4?

Step 1: Write down the two equations of the lines: y = 2x + 1 and y = -x + 4.
Step 2: Set the two equations equal to each other because at the point of intersection, both y values are the same: 2x + 1 = -x + 4.
Step 3: Solve for x. First, add x to both sides: 2x + x + 1 = 4.
Step 4: Combine like terms: 3x + 1 = 4.
Step 5: Subtract 1 from both sides: 3x = 3.
Step 6: Divide both sides by 3 to find x: x = 1.
Step 7: Now that we have x, substitute it back into one of the original equations to find y. Use y = 2x + 1: y = 2(1) + 1.
Step 8: Calculate y: y = 2 + 1 = 3.
Step 9: The point of intersection is (x, y), which is (1, 3).

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