Find the point of intersection of the lines 2x + 3y = 6 and x - y = 1. (2020)

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Question: Find the point of intersection of the lines 2x + 3y = 6 and x - y = 1. (2020)

Options:

Correct Answer: (1, 1)

Exam Year: 2020

Solution:

Solving the equations simultaneously, we find the intersection point is (1, 1).

Find the point of intersection of the lines 2x + 3y = 6 and x - y = 1. (2020)

Find the point of intersection of the lines 2x + 3y = 6 and x - y = 1. (2020)

Step 1: Write down the two equations: 2x + 3y = 6 and x - y = 1.
Step 2: Solve the second equation (x - y = 1) for x. This gives us x = y + 1.
Step 3: Substitute x = y + 1 into the first equation (2x + 3y = 6).
Step 4: Replace x in the first equation: 2(y + 1) + 3y = 6.
Step 5: Simplify the equation: 2y + 2 + 3y = 6.
Step 6: Combine like terms: 5y + 2 = 6.
Step 7: Subtract 2 from both sides: 5y = 4.
Step 8: Divide both sides by 5: y = 4/5.
Step 9: Now, substitute y = 4/5 back into x = y + 1 to find x: x = 4/5 + 1 = 4/5 + 5/5 = 9/5.
Step 10: The point of intersection is (9/5, 4/5).

Simultaneous Equations – The question tests the ability to solve two linear equations simultaneously to find their point of intersection.
Graphical Interpretation – Understanding how to interpret the intersection of two lines graphically as the solution to the system of equations.