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

nitraiddQ 2021-02-21 Answered
Solve the given system of equations by matrix equation.
5x-4y=4
3x-2y=3
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Expert Answer

oppturf
Answered 2021-02-23 Author has 94 answers

Step 1
Given,
System of equations is
5x-4y=4
3x-2y=3
system of equations in matrix form can be written as:
AX=BX=A1B
Step 2
Here,A=[5432],B=[43],X=[xy]
Formula for A1 is:
A1=1detAadj A
Now,
detA=5(2)(4)(3)
=-10+12
=2
And,
adj A=[2435]
So,
A1=12[2435]
Step 3
Thus, the solution of the given system of equations is
X=A1B
[xy]=12[2435][43]
[xy]=12[2(4)+4(3)3(4)+5(3)]
[xy]=12[8+1212+15]
[xy]=12[43]
[xy]=[21.5]
Step 4
Therefore,
The solution of the given system of equations is
x = 2
y = 1.5

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Jeffrey Jordon
Answered 2021-11-19 Author has 2313 answers

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