Solve two or three simultaneous equations (linear systems) without elimination by hand.
In short: Solving a system of equations on the GDC means entering the coefficients of simultaneous equations into the equation solver or a matrix and reading off the solution. It works for two or three unknowns and is quick when the numbers are messy. Always check your answers by substituting them back into the original equations.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | APPS → PlySmlt2 → Simultaneous Eqn Solver; set the number of equations/unknowns and enter the coefficients. | Main menu → Equation → Simultaneous, set the number of unknowns, enter the coefficients, SOLVE. | menu → Algebra → Solve System of Equations, or use linSolve. |
Tip: No solution or infinitely many? The calculator will flag it - that means the lines/planes are parallel or coincident.
Tip: No solution or infinitely many? The calculator will flag it - that means the lines/planes are parallel or coincident.
Tip: No solution or infinitely many? The calculator will flag it - that means the lines/planes are parallel or coincident.
Here's a real IB-style question that uses exactly this technique.
Solve the system: 2x + y − z = 5, x − y + 2z = 0, 3x + 2y + z = 10.
Solve two or three simultaneous equations (linear systems) without elimination by hand. Two or three linear equations need solving simultaneously and elimination by hand would be slow. A word problem sets up several unknowns with several linear conditions.
1. Write each equation in the form ax + by (+ cz) = d. 2. APPS → PlySmlt2 → Simultaneous Eqn Solver; set the number of equations/unknowns and enter the coefficients.
1. Write each equation in the form ax + by (+ cz) = d. 2. Main menu → Equation → Simultaneous, set the number of unknowns, enter the coefficients, SOLVE.
1. Write each equation in the form ax + by (+ cz) = d. 2. menu → Algebra → Solve System of Equations, or use linSolve.
No solution or infinitely many? The calculator will flag it - that means the lines/planes are parallel or coincident.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: Enter the coefficients of the 3×3 linear system; A1: x = 2, y = 1, z = 1.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.