Answer :
Answer: e= x + y = 10
Step-by-step explanation :
check out the attachment for the answer
We got the value of [tex]e=\frac{78}{7}[/tex] by solving the given equations [tex]3x+2y=26[/tex] and [tex]5x+y=26[/tex] by reduction method.
What is reduction method?
The reduction or elimination approach includes using arithmetic operations between equations to produce equivalent equations with fewer unknowns that are simpler to analyze and evaluate.
Given equations are
[tex]3x+2y=26[/tex] .........(1)
[tex]5x+y=26[/tex] ...........(2)
We need to find the value of [tex]e=x+y[/tex]
Simplifying the given equation (2) and we get
[tex]5x+y=26\\\Rightarrow y=26-5x[/tex]................(3)
Now, substitute the equation (3) in equation (1) and we get
[tex]3x+2(26-5x)=26\\\Rightarrow 3x+52-10x=26\\\Rightarrow -7x+52=26\\\Rightarrow -7x=26-52\\\Rightarrow -7x=-26\\\Rightarrow x=\frac{26}{7}[/tex]
Substitute the value of x in equation (3), we get
[tex]y=26-5\frac{26}{7} \\\Rightarrow y=26-\frac{110}{7}\\\Rightarrow y=\frac{162-110}{7}\\\Rightarrow y=\frac{52}{7}\\[/tex]
Now adding the values of x and y, we get
[tex]\therefore e=\frac{26}{7}+\frac{52}{7}\\\Rightarrow e=-{[\frac{26+52}{7}]\\\Rightarrow e={[\frac{78}{7}][/tex]
Therefore, the value of [tex]e=\frac{78}{7}[/tex].
To learn more about reduction method from the below link:
https://brainly.com/question/13107448
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