For the solution [tex](3,\frac{1}{3})[/tex] of the given system of equations, the value of x - y is [tex]2\frac{2}{3}[/tex]
To determine the value of x - y, we will solve the two equations simultaneously
We have
7x + 3y = 8 ------ (1)
6x – 3y = 5 ----- (2)
Solving by the elimination method
Add equations (1) and (2) together
We get
[tex]7x + 6x +3y -3y = 8 + 5[/tex]
Then,
[tex]13x = 13[/tex]
Now, divide both sides by 13
[tex]\frac{13x}{13} = \frac{13}{13}[/tex]
∴ [tex]x = 1[/tex]
Now, substitute the value of x into equation (1)
[tex]7x + 3y = 8[/tex]
We get
[tex]7(1) + 3y = 8[/tex]
[tex]7 + 3y = 8[/tex]
[tex]3y = 8-7[/tex]
Then,
[tex]3y = 1[/tex]
Divide both sides by 3
[tex]\frac{3y}{3} =\frac{1}{3}[/tex]
∴ [tex]y = \frac{1}{3}[/tex]
The solution to the system of equations is [tex](3,\frac{1}{3})[/tex]
Now, for the value of x - y, we will input the values of x and y
That is,
[tex]x -y = 3 -\frac{1}{3}[/tex]
[tex]= 2\frac{2}{3}[/tex]
∴ [tex]x-y =2\frac{2}{3}[/tex]
Hence, the value of x - y is [tex]2\frac{2}{3}[/tex]
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