Question

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equation Cramer's rule: -
3x - 2y=5
x - 3y = -3​

Answer 1

The solution of equations are x= 3 and y= 2.

Given:

• $3x - 2y = 5$ and $x - 3y = - 3$

To find:

• Solution of equations using Cramer's rule.

Solution:

Formula/Concept to be used:

Cramer's rule:The rule says that

x=Δ1/Δ

y=Δ2/Δ

where Δ is determinant of matrix A and Δ1,Δ2 are the determinant of A when column 1,2 are replaced by coefficient matrix respectively.

Step 1:

Write the equations in matrix form.

AX=B

$\left[\begin{array}{cc}3&-2\\1&-3\end{array}\right]\left[\begin{array}{cc}x\\y\end{array}\right] =\left[\begin{array}{cc}5\\ - 3\end{array}\right]$

Step 2:

Find the determinant of matrix A.

$\Delta = \left |\begin{array}{cc}3&-2\\1&-3\end{array}\right |$

or

$\Delta = - 9 + 2$

or

$\Delta = - 7$

Step 3:

Find the determinant of matrix A1 and A2.

$\Delta_1 = \left |\begin{array}{cc}5&-2\\ - 3&-3\end{array}\right |$

or

$\Delta_1 = - 15 - 6$

or

$\Delta_1 = - 21$

By the same way

$\Delta_2 = \left[\begin{array}{cc}3&5\\1&-3\end{array}\right]$

or

$\Delta_2 = - 9 - 5$

or

$\Delta_2 = - 14$

Step 4:

Find the value of x and y.

$x = \frac{\Delta_1}{\Delta}$

or

$x = \frac{ - 21}{ - 7}$

or

$\bf \red{x = 3}$

and

$y = \frac{\Delta_2}{\Delta}$

or

$y = \frac{ - 14}{ - 7}$

or

$\bf \red{y = 2 }$

Thus,

Solution of equations are x= 3 and y= 2.

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