How Do You Use Technology to Solve a System of Linear Equations in Up to 3 Variables?

Use a graphic display calculator (GDC) to enter the coefficients and constants into a simultaneous-equation solver or matrix calculation, then read the unique solution. In IB Mathematics: Applications and Interpretation, technology is expected for systems containing up to three variables.

The Method

First, rearrange every equation into the same standard form:

$$a x+b y+c z=d$$

Before opening the solver, identify each coefficient's sign carefully. For example, (-y) has coefficient $-1$, not $1$. Keep the equations in their original row order; only the variable order must stay consistent across every row. This prevents most data-entry errors.

The coefficients must be entered in a consistent variable order, usually (x,y,z). If a variable is absent, enter a coefficient of $0$.

For example, solve:

$$\begin{aligned} x+y+z&=6\\ 2x-y+z&=6\\ -x+3y+2z&=7 \end{aligned}$$

Enter the coefficient matrix and constant vector as:

$$A=\begin{pmatrix}1&1&1\\2&-1&1\\-1&3&2\end{pmatrix},\qquad B=\begin{pmatrix}6\\6\\7\end{pmatrix}$$

The GDC gives:

$$\begin{pmatrix}x\\y\\z\end{pmatrix} = \begin{pmatrix}2\\1\\3\end{pmatrix}$$

Therefore, $x=2$, $y=1$, and $z=3$. Verify the result by substituting it into at least one original equation, for example $2+1+3=6$.

To verify completely, substitute the solution into all three original equations. The remaining checks are $2(2)-1+3=6$ and $-2+3(1)+2(3)=7$. If any check fails, inspect negative signs, missing zero coefficients, and the constant column before recalculating.

A common misconception is that entering only the final answers demonstrates the method. It does not: incorrect coefficient order can produce a plausible but wrong result, so show the equations in standard form or display the matrix setup.

Exam Technique

This is SL 1.8, common to both SL and HL. All Mathematics AI papers are GDC-active, and examination systems will have a unique solution. For a command term such as solve, show the technology setup and state the complete ordered solution, rather than giving an unexplained calculator output.