# How do you solve 3x+4y=2 and x-y+6?

Apr 18, 2018

This is presumably meant to be simple pair of linear simultaneous equations easily solved. The problem is the second one isn't equation; let's guess about what equation was meant:

$3 x + 4 y = 2$

$x - y = 6$

Multiplying that equation by $4 ,$

$4 x - 4 y = 24$

$7 x = 26$

$x = \frac{26}{7}$

Multiplying the second equation by three:

$3 x - 3 y = 18$

Subtracting from the first,

$7 y = - 16$

$y = - \frac{16}{7}$

Check:

$x - y = \frac{26}{7} - - \frac{16}{7} = \frac{42}{7} = 6 \setminus \quad \setminus \sqrt{}$

$3 x + 4 y = 1 7 \left(3 \left(26\right) + 4 \left(- 16\right)\right) = 2 \setminus \quad \setminus \sqrt{}$

Remember we had to guess the equation to start, so this might not be the exact problem the student is trying to answer.