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Worked Examples · Example 4

Q.Using Cramer's Rule, solve the system of equations 2x+y=72x+y=7 and x−y=2x-y=2.

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Forming DD

D=∣211−1∣=2(−1)−1(1)=−2−1=−3D=\begin{vmatrix}2&1\\1&-1\end{vmatrix}=2(-1)-1(1)=-2-1=-3

Since D≠0D\neq0, a unique solution exists.

Forming DxD_x (replace the xx-coefficient column with the constants 7, 2)

Dx=∣712−1∣=7(−1)−1(2)=−7−2=−9D_x=\begin{vmatrix}7&1\\2&-1\end{vmatrix}=7(-1)-1(2)=-7-2=-9

Forming DyD_y (replace the yy-coefficient column with the constants 7, 2)

Dy=∣2712∣=2(2)−7(1)=4−7=−3D_y=\begin{vmatrix}2&7\\1&2\end{vmatrix}=2(2)-7(1)=4-7=-3

Solving …

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←Previous questionExample 3 — Find the value(s) of x for which x3; 2x-1 =0.→Next questionExample 5 — Using Cramer's Rule, solve the system of equations 3x+2y=4 and x-3y=5.