$5 x + 5 y = 40, x + y = 8$ $5x+5y=40, x+y=8$ . What is the solution?

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Answer 1 · 2018-03-04T21:01:27

${8-t,t|tinRR}$

We have the following system of equations

${: (5x+5y=40), (x+y=8) :}}$

Adding $-1"/"5$ of eqn. $1$ to eqn. $2$ transforms the system into echelon form as

${:(5x+5y=40),(0=0):}}$

To find solutions, we discard the degenerate equation and solve the other equation.

$5x+5y=40$

Since $y$ is not a leading variable, we set it equal to an arbitrary variable, say $y=t$ for $tinRR$ .

We now solve for $x$

$5x+5t=40rArr5x=40-5trArrx=8-t$

So the set of solutions is ${8-t,t|tinRR}$

5x+5y=40, x+y=85x+5y=40,x+y=85x+5y=40, x+y=8. What is the solution?