Find the point of intersection of the lines y = 2x + 1 and y = -x + 4.

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Question: Find 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 x back gives y = 3, so the point is (1, 3).

Find the point of intersection of the lines y = 2x + 1 and y = -x + 4.

Find the point of intersection of the lines y = 2x + 1 and y = -x + 4.

Step 1: Write down the two equations: y = 2x + 1 and y = -x + 4.
Step 2: Since both equations equal y, set them equal to each other: 2x + 1 = -x + 4.
Step 3: To solve for x, first add x to both sides: 2x + x + 1 = 4.
Step 4: This simplifies to 3x + 1 = 4.
Step 5: Next, subtract 1 from both sides: 3x = 4 - 1.
Step 6: This simplifies to 3x = 3.
Step 7: Now, divide both sides by 3 to find x: x = 3 / 3.
Step 8: This gives us x = 1.
Step 9: Now that we have x, substitute it back into one of the original equations to find y. Use y = 2x + 1.
Step 10: Substitute x = 1 into the equation: y = 2(1) + 1.
Step 11: This simplifies to y = 2 + 1, which gives y = 3.
Step 12: Now we have both x and y: x = 1 and y = 3.
Step 13: Therefore, the point of intersection is (1, 3).

Linear Equations – Understanding how to find the intersection of two linear equations by setting them equal to each other.
Substitution – Using the value of x found to calculate the corresponding y value.