If , find the value of x and y.

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Solving System of Linear Equation Cramers Rule

Question

If $x [\begin{array}{c} 2 \\ 3 \end{array}] + y [\begin{array}{c} - 1 \\ 1 \end{array}] = [\begin{array}{c} 10 \\ 5 \end{array}]$ , find the value of x and y.

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Given,

x [\begin{array}{c} 2 \\ 3 \end{array}] + y [\begin{array}{c} - 1 \\ 1 \end{array}] = [\begin{array}{c} 10 \\ 5 \end{array}]

From this matrix equation we get,

2x – y = 10 .....(1) and 3x + y = 5 .....(2).

Now adding (1) and (2) we get,

5x = 15

or, x = 3.

Now putting this in (1) we get, y = – 4.