Chapter 4: Q3. (page 192)

Write a system of equations whose solution is
$x = \frac{|\begin{matrix} - 6 & 5 \\ 30 & - 2 \end{matrix}|}{|\begin{matrix} 3 & 5 \\ 4 & - 2 \end{matrix}|}$ $y = \frac{|\begin{matrix} 3 & - 6 \\ 4 & 30 \end{matrix}|}{|\begin{matrix} 3 & 5 \\ 4 & - 2 \end{matrix}|}$

Short Answer

Expert verified

The required system of equations is,

$3 x + 5 y = - 6$

$4 x - 2 y = 30$

Step by step solution

Step 1- Determine the approach that can be used

Using the Cramer’s rule for the value of x that is $x = \frac{|\begin{matrix} e & b \\ f & d \end{matrix}|}{|\begin{matrix} a & b \\ c & d \end{matrix}|}$ and comparing it with the provided value of x can help.

– Form the system of equations by using the approach

Use the obtained approach and determine the value of a, b, c, d, e and f.

The obtained values are $a = 3$ , $b = 5$ , $c = 4$ , $d = - 2$ , $e = - 6$ and $f = 30$ .

Use the obtained values and form the equations in the form of $a x + b y = e$ and $c x + d y = f$ .

$3 x + 5 y = - 6$

$4 x - 2 y = 30$

Step 3- Make the conclusion

As the obtained system of equations is representing the values which are in provided system of equations which means that the obtained equations are the required equations.

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Write a system of equations whose solution is
$x = \frac{|\begin{matrix} - 6 & 5 \\ 30 & - 2 \end{matrix}|}{|\begin{matrix} 3 & 5 \\ 4 & - 2 \end{matrix}|}$ $y = \frac{|\begin{matrix} 3 & - 6 \\ 4 & 30 \end{matrix}|}{|\begin{matrix} 3 & 5 \\ 4 & - 2 \end{matrix}|}$

Short Answer

Step by step solution

Step 1- Determine the approach that can be used

– Form the system of equations by using the approach

Step 3- Make the conclusion

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Write a system of equations whose solution isx=−6530−2354−2y=3−6430354−2

Short Answer

Step by step solution

Step 1- Determine the approach that can be used

– Form the system of equations by using the approach

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write a system of equations whose solution is
$x = \frac{|\begin{matrix} - 6 & 5 \\ 30 & - 2 \end{matrix}|}{|\begin{matrix} 3 & 5 \\ 4 & - 2 \end{matrix}|}$ $y = \frac{|\begin{matrix} 3 & - 6 \\ 4 & 30 \end{matrix}|}{|\begin{matrix} 3 & 5 \\ 4 & - 2 \end{matrix}|}$