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Chapter 4: Q23. (page 157)

Solve each equation.
$[\begin{matrix} 4 x \\ y - 1 \end{matrix}] = [\begin{matrix} 11 + 3 y \\ x \end{matrix}]$

Short Answer

Expert verified

The solution is $(14, 15)$ .

Step by step solution

01

– Description of step.

As the matrices are equal, the corresponding elements are equal. Write the two linear equations to show this equality.

$\begin{matrix} 4 x = 11 + 3 y \\ y 鈭� 1 = x \end{matrix}$

02

– Description of step.

Substitute $y - 1$ for x into $4 x = 11 + 3 y$ and simplify.

$\begin{matrix} 4 (y 鈭� 1) = 11 + 3 y \\ 4 y 鈭� 4 = 11 + 3 y \\ 4 y 鈭� 3 y = 11 + 4 \\ y = 15 \end{matrix}$

03

– Description of step.

Substitute $15$ for y into $y - 1 = x$ and simplify to find the value of x.

$\begin{matrix} y 鈭� 1 = x \\ 15 鈭� 1 = x \\ 14 = x \end{matrix}$

Therefore, the solution is $(14, 15)$ .

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