Question

Solve the following system of equations using cross multiplication method :

2x + 7y - 5 = 0

-3x + 8y = -11

Solve the following system of equations using cross multiplication method :

3x + 4y = 24

20x - 11y = 47

Answer 1

Dear Student,

$$\begin{gathered} 2\mathrm{x}+7\mathrm{y}-5=0 \\ -3\mathrm{x}+8\mathrm{y}=-11 \\ \mathrm{Compairing}\mathrm{with}{\mathrm{a}}_1\mathrm{x}+{\mathrm{b}}_1\mathrm{y}+{\mathrm{c}}_1=0\mathrm{and}{\mathrm{a}}_2\mathrm{x}+{\mathrm{b}}_2\mathrm{y}+{\mathrm{c}}_2=0,\mathrm{we}\mathrm{get} \\ {\mathrm{a}}_1=2,{\mathrm{b}}_1=7,{\mathrm{c}}_1=-5 \\ {\mathrm{a}}_2=-3,{\mathrm{b}}_2=8,{\mathrm{c}}_2=11 \\ \mathrm{Using}\mathrm{Cross}\mathrm{multiplication}\mathrm{method}, \\ \frac{\mathrm{x}}{{\mathrm{b}}_1{\mathrm{c}}_2-{\mathrm{b}}_2{\mathrm{c}}_1}=\frac{\mathrm{y}}{{\mathrm{a}}_2{\mathrm{c}}_1-{\mathrm{a}}_1{\mathrm{c}}_2}=\frac{1}{{\mathrm{a}}_1{\mathrm{b}}_2-{\mathrm{a}}_2{\mathrm{b}}_1} \\ \frac{\mathrm{x}}{\left(7\times 11\right)-\left(8\times -5\right)}=\frac{\mathrm{y}}{\left(-5\times -3\right)-2\times 11}=\frac{1}{\left(2\times 8\right)-\left(-3\times 7\right)} \\ \frac{\mathrm{x}}{117}=\frac{\mathrm{y}}{-7}=\frac{1}{37} \\ \mathrm{So},\mathrm{x}=\frac{117}{37}\mathrm{and}\mathrm{y}=\frac{-7}{37} \end{gathered}$$

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