Find the point of intersection of the lines y = x + 2 and y = -x + 4. (2023)

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Question: Find the point of intersection of the lines y = x + 2 and y = -x + 4. (2023)

Options:

Correct Answer: (1, 3)

Exam Year: 2023

Solution:

Setting x + 2 = -x + 4 gives 2x = 2, so x = 1. Substituting x back gives y = 3. Thus, the point is (1, 3).

Find the point of intersection of the lines y = x + 2 and y = -x + 4. (2023)

Find the point of intersection of the lines y = x + 2 and y = -x + 4. (2023)

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

Linear Equations – Understanding how to solve systems of linear equations by setting them equal to each other.
Substitution Method – Using substitution to find the value of one variable in terms of another.
Graphical Interpretation – Interpreting the intersection of two lines as the solution to the system of equations.