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Solve each of the following systems of equations using matrix method.
5x + 2y = 4;
7x + 3y = 5.
CBSE | Class 12 | Excercise 8A | Maths | RS Aggarwal | System of Linear Equations
Solve each of the following systems of equations using matrix method.
5x + 2y = 4;
7x + 3y = 5.

Solution:

We need to find: -\mathrm{x}, \mathrm{y}
The given set of lines are : –
\begin{array}{l} 5 x+2 y=4 \\ 7 x+3 y=5 \end{array}
On converting the following equations in matrix form,
\begin{array}{l} A X=B \\ \left(\begin{array}{ll} 5 & 2 \\ 7 & 3 \end{array}\right)\left(\begin{array}{l} x \\ y \end{array}\right)=\left(\begin{array}{l} 4 \\ 5 \end{array}\right) \\ 5 R_{2}-7 R_{1} \\ \left(\begin{array}{ll} 5 & 2 \\ 0 & 1 \end{array}\right)\left(\begin{array}{l} x \\ y \end{array}\right)=\left(\begin{array}{c} 4 \\ -3 \end{array}\right) \end{array}
Again on converting back into equation form, we obtain
\begin{array}{l} 5 x+2 y=4 \\ y=-3 \\ 5 x+2 \times-3=4 \\ 5 x=10 \\ x=2 \\ \therefore x=2, y=-3 \end{array}

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