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

₹0.0

Question: Determine 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, hence x = 1. Substituting back gives y = 3.

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

Determine 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 = 3.
Step 6: Now, divide both sides by 3 to find x: x = 1.
Step 7: Substitute x = 1 back into one of the original equations to find y. Using y = 2x + 1: y = 2(1) + 1.
Step 8: This simplifies to y = 2 + 1, so y = 3.
Step 9: 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.