Mathematics: The graph shows the number of gallons of white paint that were mixed with gallons of orange paint in various different ratios: The number of gallons of white paint mixed with 1 gallon of orange paint is ______.

The graph shows the number of gallons of white

Hellokittyjam35

25.09.2020

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)

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