# How do you solve the simultaneous equations x+2y=4 and 3x-4y=7?

Aug 9, 2015

$x = 3$
$y = \frac{1}{2}$

#### Explanation:

$x + 2 y = 4$
$3 x - 4 y = 7$

Solve the first equation for $x$
$x = 4 - 2 y$

Substitute the value of $x$ into the second equation.
$3 \left(4 - 2 y\right) - 4 y = 7$

Now there is only one variable present, so we can solve for $y$.
$12 - 6 y - 4 y = 7$
$- 10 y = 7 - 12$
$y = \left(- \frac{5}{-} 10\right)$
$y = \frac{1}{2}$

Finally, substitute the value of $y$ into the first equation again
$x + 2 \cdot \frac{1}{2} = 4$
$x + 1 = 4$
$x = 4 - 1 = 3$#