Find the point of intersection of the lines y = x + 1 and y = -x + 5.

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Question: Find the point of intersection of the lines y = x + 1 and y = -x + 5.

Options:

Correct Answer: (2, 3)

Solution:

Set x + 1 = -x + 5. Solving gives x = 2, y = 3. Thus, the point is (2, 3).

Find the point of intersection of the lines y = x + 1 and y = -x + 5.

Find the point of intersection of the lines y = x + 1 and y = -x + 5.

Correct Answer: (2, 3)

Step 1: Write down the two equations: y = x + 1 and y = -x + 5.
Step 2: Since both equations equal y, set them equal to each other: x + 1 = -x + 5.
Step 3: Solve for x. First, add x to both sides: x + x + 1 = 5.
Step 4: This simplifies to 2x + 1 = 5.
Step 5: Next, subtract 1 from both sides: 2x = 4.
Step 6: Now, divide both sides by 2: x = 2.
Step 7: Now that we have x, substitute x = 2 back into one of the original equations to find y. Use y = x + 1: y = 2 + 1.
Step 8: This gives us y = 3.
Step 9: Now we have both x and y. The point of intersection is (2, 3).

Linear Equations – Understanding how to find the intersection of two linear equations by setting them equal to each other.
Substitution Method – Using substitution to solve for variables in equations.