Determine the value of (x + y) if

Engineering

Mathematics

Introduction to Matrix

Solving System of Linear Equation Cramers Rule

Question

Determine the value of (x + y) if $[\begin{array}{cc} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{array}] = [\begin{array}{cc} 7 & 7 y - 12 \\ y & x + 6 \end{array}]$

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[\begin{array}{cc} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{array}] = [\begin{array}{cc} 7 & 7 y - 12 \\ y & x + 6 \end{array}]

Comparing the corresponding rows and columns,

4x = x + 6

⇒ 4x – x = 6

⇒ 3x = 6 or

x = \frac{6}{3} = 2

Again, 5x – 7 = y

⇒ 5 × 2 – 7 = y since x = 2

∴ y = 10 – 7 = 3

Hence x = 2, y = 3