How do you solve the system : $2 x + 6 y = 5$ $2x+6y=5$ , $8 x + 24 y = 20$ $8x+24y=20$ ?

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How do you solve the system : $2 x + 6 y = 5$ $2x+6y=5$ , $8 x + 24 y = 20$ $8x+24y=20$ ?

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Answer 1 · 2017-08-23T02:02:35

Infinitely many solutions

Explanation:

Hello there!

$2 x + 6 y = 5$ $2x + 6y = 5$
$8 x + 24 y = 20$ $8x + 24y = 20$

You can solve the system by using the elimination form or you can use the substitution form. I like substitution so I'll use it :)

We need to solve $2 x + 6 y = 5$ $2x + 6y = 5$ for x
$2 x + 6 y = 5$ $2x + 6y = 5$
$2 x = - 6 y + 5$ $2x = -6y + 5$
Divide both sides by 2
$\frac{2 x}{2}$ $(2x)/2$ = $\frac{- 6 y + 5}{2}$ $(-6y+5)/2$
$x$ $x$ = $- 3 y$ $-3y$ + $\frac{5}{2}$ $5/2$
Now substitute $- 3 y$ $-3y$ + $\frac{5}{2}$ $5/2$ for $x$ $x$ in $8 x + 24 y = 20$ $8x +24y = 20$
$8$ $8$ $(- 3 y + \frac{5}{2})$ $(-3y + 5/2)$ + $24 y = 20$ $24y = 20$
Distribute
$(8) (- 3 y) + (8) (\frac{5}{2}) + 24 y = 20$ $(8)(-3y) + (8)(5/2) + 24y = 20$
$- 24 y + 20 + 24 y_{=} 20$ $-24y + 20 + 24y_ = 20$
$20 = 20$ $20 = 20$
Add -20 to both sides
$20 - 20 = 20 - 20$ $20 - 20 = 20 - 20$
$0 = 0$ $0 = 0$
Final answer: All real numbers are solutions

I hope I helped!

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How do you solve the system : $2 x + 6 y = 5$ $2x+6y=5$ , $8 x + 24 y = 20$ $8x+24y=20$ ?

1 Answer

Explanation:

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