# Use Cramer's rule to solve the following system of equations. If D = 0, use another method to solve the system. 2x + 3y = 4 4x - 6y = 8

Use Cramers
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Step 1
Given: The system of equations is
2x+3y=4
4x-6y=8
Step 2
Solution:
Obtain the value of D as follows.
$D|\begin{array}{cc}2& 3\\ 4& -6\end{array}|$
=2(-6)-(3)(4)
=-12-12
$=-24\ne 0$
As D is not equal to zero, the unique solution exists.
Step 3
Obtain the value of ${D}_{1}$ as follows.
${D}_{1}=|\begin{array}{cc}4& 3\\ 8& -6\end{array}|$
=(4)(-6)-3(8)
=-24-24
=-48
Step 4
Obtain the value of ${D}_{2}$ as follows.
${D}_{2}=|\begin{array}{cc}2& 4\\ 4& 8\end{array}|$
=2(8)-(4)(4)
=16-16
=0
Step 5
Thus, the value of x and y by Cramer’s rule becomes
$x=\frac{{D}_{1}}{D}=\frac{-48}{-24}=2$
$y=\frac{{D}_{2}}{D}=\frac{0}{-24}=0$
Step 6
Therefore, the solution of the system of equations is
x=2 and y =0
Jeffrey Jordon