System Intersections Game
Find where two straight-line equations intersect by solving simultaneous linear equations.
Math puzzle challenges
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Instructions, device progress and accessibility
Select Easy, Normal, or Hard; choose a UTC Daily challenge or unlimited Practice. Solve every algebra problem, then press Check answer. Hints and Undo mark the round as assisted. Scores and completed challenges save locally on your device when available.
Local progress is checked when play begins.
How to play System Intersections
Find where two straight-line equations intersect by solving simultaneous linear equations. Start with Easy and move toward Hard when confident. Enter exact answers, including negative values where needed. Use your keyboard or touch controls, and check the answer before requesting a hint.
Understand the mathematics
For y = 2x + 1 and y = −x + 7, set 2x + 1 = −x + 7. Then 3x = 6, x = 2 and y = 5.
Each practice puzzle generates a new set of algebra questions. The daily challenge is consistent for the same date and difficulty, allowing fair repeat practice.
Worked example
For y = 2x + 1 and y = −x + 7, set 2x + 1 = −x + 7. Then 3x = 6, x = 2 and y = 5.
Tips for accurate algebra
Set the right-hand sides equal, solve for x, then substitute that x in either line to calculate y. Check negative values, follow order of operations, and verify the solution against the question.
Frequently asked questions
What is the intersection of two lines?
It is the ordered pair (x, y) that satisfies both line equations simultaneously.
How can I verify my answer?
Substitute your x and y into both original equations; both must be true.