Linear Equations in Two Variables Practice
Solve chapter-level practice questions for Linear Equations in Two Variables with reveal-only solutions and quick revision support.
Practice Set 1 — Solutions of Linear Equations
Standard form, finding ordered-pair solutions, checking solutions.
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Practice Set 2 — Graphs and Special Lines
Drawing graphs, intercepts, and lines parallel to the axes.
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Quick Q&A Before You Revise
How many solutions does a linear equation in two variables have?
Infinitely many when a and b are not both zero. If b is non-zero, each x determines one y. If b = 0, x is fixed and y can be any real number. Each solution pair is a point on the line.
Why is the graph of ax + by + c = 0 always a straight line?
If b is non-zero, rearrange to y = -(a/b)x - c/b, a straight line with constant slope. If b = 0, then a is non-zero and x = -c/a is a vertical straight line.
Is x = 5 a linear equation in one variable or two?
It depends on context. On the number line it locates one point. In the Cartesian plane it is treated as 1·x + 0·y = 5 and its graph is a vertical line.
How many points are needed to draw the graph of a linear equation?
Two points are enough to fix a line, but it is good practice to plot a third point as a check that all three are collinear.