# Solve the given system of equations by matrix equation. 5x-4y=4 3x-2y=3

Solve the given system of equations by matrix equation.
5x-4y=4
3x-2y=3
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

oppturf

Step 1
Given,
System of equations is
5x-4y=4
3x-2y=3
system of equations in matrix form can be written as:
$AX=B⇒X={A}^{-1}B$
Step 2
Here,$A=\left[\begin{array}{cc}5& -4\\ 3& -2\end{array}\right],B=\left[\begin{array}{c}4\\ 3\end{array}\right],X=\left[\begin{array}{c}x\\ y\end{array}\right]$
Formula for ${A}^{-1}$ is:
${A}^{-1}=\frac{1}{detA}$adj A
Now,
$detA=5\left(-2\right)-\left(-4\right)\left(3\right)$
=-10+12
=2
And,
adj $A=\left[\begin{array}{cc}-2& 4\\ -3& 5\end{array}\right]$
So,
${A}^{-1}=\frac{1}{2}\left[\begin{array}{cc}-2& 4\\ -3& 5\end{array}\right]$
Step 3
Thus, the solution of the given system of equations is
$X={A}^{-1}B$
$\left[\begin{array}{c}x\\ y\end{array}\right]=\frac{1}{2}\left[\begin{array}{cc}-2& 4\\ -3& 5\end{array}\right]\left[\begin{array}{c}4\\ 3\end{array}\right]$
$\left[\begin{array}{c}x\\ y\end{array}\right]=\frac{1}{2}\left[\begin{array}{c}-2\left(4\right)+4\left(3\right)\\ -3\left(4\right)+5\left(3\right)\end{array}\right]$
$\left[\begin{array}{c}x\\ y\end{array}\right]=\frac{1}{2}\left[\begin{array}{c}-8+12\\ -12+15\end{array}\right]$
$\left[\begin{array}{c}x\\ y\end{array}\right]=\frac{1}{2}\left[\begin{array}{c}4\\ 3\end{array}\right]$
$\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}2\\ 1.5\end{array}\right]$
Step 4
Therefore,
The solution of the given system of equations is
x = 2
y = 1.5

Jeffrey Jordon