How do you solve the following system: -2x + 5y = 20, 2x – 5y = 5 ?

Mar 4, 2018

No solution

Explanation:

Some( in fact many) system of equations doesn't have answers... as you'll solve this you'll always get $20 = 5$ which is impossible

it is useful in ${11}^{t h}$ standard... so wait till then

Mar 4, 2018

No solutions

Explanation:

$- 2 x + 5 y = 20$
$2 x - 5 y = 5$

We need to solve $- 2 x + 5 y = 20$ for $x$

$- 2 x + 5 y = 20$

$- 2 x = 20 - 5 y$

$x = \frac{20 - 5 y}{- 2}$

$x = \frac{5}{2} y - 10$

Now we can substitute $\frac{5}{2} y - 10$ for $x$ in $2 x - 5 y = 5$

$2 x - 5 y = 5$

$2 \left(\frac{5}{2} y - 10\right) - 5 y = 5$

Distribute

$\left(2\right) \left(\frac{5}{2} y\right) + \left(2\right) \left(- 10\right) - 5 y = 5$

$\left(\frac{10}{2} y\right) - 20 - 5 y = 5$

$5 y - 20 - 5 y = 5$

Combine like terms

$\cancel{5 y} \cancel{- 5 y} - 20 = 5$

$- 20 = 5$

Add $20$ to both sides

$- 20 + 20 = 5 + 20$

$0 = 25$

Thus,

There are no solutions!