# 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 Question
Equations 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 2020-12-01
Step 1
Given: The system of equations is
2x+3y=4
4x-6y=8
Step 2
Solution:
Obtain the value of D as follows.
$$\displaystyle{D}{\left|\begin{array}{cc} {2}&{3}\\{4}&-{6}\end{array}\right|}$$
=2(-6)-(3)(4)
=-12-12
$$\displaystyle=-{24}\ne{0}$$
As D is not equal to zero, the unique solution exists.
Step 3
Obtain the value of $$\displaystyle{D}_{{1}}$$ as follows.
$$\displaystyle{D}_{{1}}={\left|\begin{array}{cc} {4}&{3}\\{8}&-{6}\end{array}\right|}$$
=(4)(-6)-3(8)
=-24-24
=-48
Step 4
Obtain the value of $$\displaystyle{D}_{{2}}$$ as follows.
$$\displaystyle{D}_{{2}}={\left|\begin{array}{cc} {2}&{4}\\{4}&{8}\end{array}\right|}$$
=2(8)-(4)(4)
=16-16
=0
Step 5
Thus, the value of x and y by Cramer’s rule becomes
$$\displaystyle{x}=\frac{{D}_{{1}}}{{D}}=\frac{{-{48}}}{{-{24}}}={2}$$
$$\displaystyle{y}=\frac{{D}_{{2}}}{{D}}=\frac{{0}}{{-{24}}}={0}$$
Step 6
Therefore, the solution of the system of equations is
x=2 and y =0

### Relevant Questions Use Cramer’s Rule to solve (if possible) the system of linear equations.
4x-y-z=1
2x+2y+3z=10
5x-2y-2z=-1 Consider the following system of llinear equations.
$$\displaystyle\frac{{1}}{{3}}{x}+{y}=\frac{{5}}{{4}}$$
$$\displaystyle\frac{{2}}{{3}}{x}-\frac{{4}}{{3}}{y}=\frac{{5}}{{3}}$$
Part A: $$\displaystyle\frac{{{W}\hat{\propto}{e}{r}{t}{y}}}{{\propto{e}{r}{t}{i}{e}{s}}}$$ can be used to write an equivalent system?
Part B: Write an equivalent system and use elimination method to solve for x and y. Solve the following system of linear equations in two variables by Substitution method.
x=8-2y
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x-2y=-8
(a)Use the substitution method to justify that the given system of equations has no solution.
(b)What do you know about the two lines in this system of equations? Use Cramer’s Rule to solve the system of linear equations.
20x+8y=11
12x-24y=21 Use the method of substitution to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
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x+2y=7 What is the correct first step to slove this system of equations 4x-3y=-10
2x+3y=4   