Find the point of intersection of the lines 2x + y = 10 and x - y = 1. (2020)

Find the point of intersection of the lines 2x + y = 10 and x - y = 1. (2020)

Step 1: Write down the two equations: 2x + y = 10 and x - y = 1.
Step 2: Solve one of the equations for one variable. Let's solve x - y = 1 for y: y = x - 1.
Step 3: Substitute y = x - 1 into the first equation (2x + y = 10): 2x + (x - 1) = 10.
Step 4: Simplify the equation: 2x + x - 1 = 10 becomes 3x - 1 = 10.
Step 5: Add 1 to both sides: 3x = 11.
Step 6: Divide both sides by 3: x = 11/3 or x = 3.67.
Step 7: Now substitute x back into y = x - 1 to find y: y = (11/3) - 1 = (11/3) - (3/3) = 8/3 or y = 2.67.
Step 8: The point of intersection is (x, y) = (11/3, 8/3) or approximately (3.67, 2.67).

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 on a graph.