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Simultaneous Equations (H)

Tackle GCSE simultaneous equations (Higher): solve linear pairs by elimination or substitution, spot no-solution or infinite-solution cases, and interpret intersections on graphs.

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Fascinating Fact:

In a consistency test, 2x + 4y = 12 and x + 2y = 5 cannot both hold because the first equals 2 times the second but 12 ≠ 10, so no solution. Lines are parallel.

In GCSE Maths, Higher-tier simultaneous equations appear in word problems and graphs. You’ll choose elimination or substitution, handle fractions and negatives, and decide whether lines meet once, never, or overlap completely.

Key Terms

Simultaneous equations: Two equations with the same unknowns that must be true at the same time.
Elimination: Adjusting equations so one variable cancels when you add or subtract them.
Inconsistent/Dependent: Inconsistent → no solution (parallel lines). Dependent → infinitely many solutions (the equations are the same line).

Frequently Asked Questions (Click to see answers)

How do I solve simultaneous equations by elimination at GCSE Higher?

Match coefficients (by multiplying if needed), add or subtract to remove one variable, solve the remaining equation, substitute back to find the second value, then check both in the originals.

What means no solution or infinitely many solutions?

No solution: the left sides are proportional but constants differ (parallel lines). Infinitely many: each equation is a multiple of the other, so they represent the same line.

How do I solve simultaneous equations by substitution?

Rearrange one equation for a variable (e.g., x = ...), substitute into the other to get one equation in one unknown, solve it, substitute back, and check both equations.