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Question 9

Solve the following system of equations using matrices.
y = 2x – 1
6x – y = 13

(3, 5)

(-3, 5)

(5, 0)

2 Answers

2 votes
-3 and 5 are the answer
User JoelPrz
by
8.5k points
1 vote

we are given two system of equations

First equation is


y=2x-1

we can write as


-2x+y=-1

Second equation is


6x-y=13

now, we can find augmented matrix


A=\begin{pmatrix}-2&1&-1\\ 6&-1&13\end{pmatrix}

now, we can change it into reduced row echelon form

step-1: multiply the 1st row by -1/2


A=\begin{pmatrix}-1&-1/2&1/2\\ 6&-1&13\end{pmatrix}

step-2: add -6 times the 1st row to the 2nd row


A=\begin{pmatrix}-1&-1/2&1/2\\ 0&2&10\end{pmatrix}

step-3:multiply the 2nd row by 1/2


A=\begin{pmatrix}-1&-1/2&1/2\\ 0&1&5\end{pmatrix}

step-4:add 1/2 times the 2nd row to the 1st row


A=\begin{pmatrix}1&0&3\\ 0&1&5\end{pmatrix}

so, we will get


x=3,y=5

Answer is (3,5)

User Siti
by
8.6k points

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