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Which of the following equations is equivalent to x + y – 10=0?

Which Of The Following Equations Is Equivalent To X Y 100 class=

Sagot :

Checking each equation one by one.

First, take the equation 5x+5y=10

Now, take 5 commons on both sides of the equation.

[tex]5(x+y)=5(2)[/tex]

Now, cancel out 5 from both sides of the equation.

[tex]\begin{gathered} x+y=2 \\ x+y-2=0 \end{gathered}[/tex]

Hence, proved this equation is not equivalent to equation x+y-10=0.

Now, check the second equation.

[tex]\begin{gathered} 2x+2y=5 \\ 2(x+y)=5 \\ x+y=\frac{5}{2} \end{gathered}[/tex]

This equation is not equivalent to the equation x+y-10=0.

Now, check the equation third.

[tex]\begin{gathered} x+y=7 \\ x+y-7=0 \end{gathered}[/tex]

It is clear that this equation is also not equivalent to the equation x+y-10=0.

Now, check the last equation.

[tex]7x+7y=70[/tex]

Take the 7 commons from both sides of the equation.

[tex]\begin{gathered} 7(x+y)=7\times(10) \\ (x+y)=10 \\ x+y-10=0 \end{gathered}[/tex]

Hence, proved this equation is equivalent to the equation x+y-10=0.

Therefore, the given option 7x+7y=70 is correct.

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