Chapter 4: Q20. (page 157)

Solve each equation.
$[\begin{matrix} x + 3 y \\ 3 x + y \end{matrix}] = [\begin{matrix} - 13 \\ 1 \end{matrix}]$

Short Answer

Expert verified

The solution is $(2, - 5)$ .

Step by step solution

– Description of step.

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

$\begin{matrix} x + 3 y = - 13 \\ 3 x + y = 1 \end{matrix}$

– Description of step.

Multiply $3 x + y = 1$ by 3 and subtract $x + 3 y = - 13$ from the obtained equation.

$\begin{matrix} 9 x + 3 y - (x + 3 y) = 3 - (- 13) \\ 9 x + 3 y - x - 3 y = 16 \\ 8 x = 16 \end{matrix}$

– Description of step.

Divide each side of $8 x = 16$ by 8 to find the value of $x$ .

$\begin{matrix} \frac{8 x}{8} = \frac{16}{8} \\ x = 2 \end{matrix}$

– Description of step.

Substitute 2 for $x$ into $3 x + y = 1$ and simplify to find the value of $y$ .

$\begin{matrix} 3 (2) + y = 1 \\ 6 + y = 1 \end{matrix}$

– Description of step.

Subtract 6 from both the sides of $6 + y = 1$ and simplify.

$\begin{matrix} 6 + y - 6 = 1 - 6 \\ y = - 5 \end{matrix}$

Therefore, the solution is $(2, - 5)$ .

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Solve each equation.
$[\begin{matrix} x + 3 y \\ 3 x + y \end{matrix}] = [\begin{matrix} - 13 \\ 1 \end{matrix}]$

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

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Solve each equation.x+3y3x+y=-131

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Geometry

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each equation.
$[\begin{matrix} x + 3 y \\ 3 x + y \end{matrix}] = [\begin{matrix} - 13 \\ 1 \end{matrix}]$