How do you solve the following system?: $13 x - 17 y = 21, - 7 x - 4 y = - 7$ $13x -17y =21, -7x -4y = -7$

Question

1945 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-20T05:06:25

$(\frac{307}{171}, - \frac{238}{171})$ $(307/171,-238/171)$

Multiply the first equation by 7, and the other by 13.

$7 \cdot (13 x - 17 y) = 7 \cdot 21$ $7*(13x-17y) =7*21$
$91 x - 119 y = 147$ $91x-119y=147$

$13 \cdot (- 7 x - 4 y) = 13 \cdot - 7$ $13*(-7x-4y)=13*-7$
$- 91 x - 52 y = 91$ $-91x-52y=91$

Then add these two equations.

$91 x - 119 y = 147$ $91x-119y=147$
$- 91 x - 52 y = 91$ $-91x-52y=91$

$91 x - 119 y - 91 x - 52 y = 147 + 91$ $91x-119y-91x-52y=147+91$
$- 171 y = 238$ $-171y=238$
$y = - \frac{238}{171}$ $y=-238/171$

Now write $- \frac{238}{171}$ $-238/171$ instead of $y$ $y$ in one of the equations.

$- 7 x + 4 \cdot \frac{238}{171} = - 7$ $-7x+4*238/171=-7$
$x = \frac{307}{171}$ $x=307/171$

How do you solve the following system?: 13x−17y=21,−7x−4y=−713x -17y =21, -7x -4y = -7