# How do you solve 3x+y=0 and 5x+y=4?

Jun 17, 2018

$x = 2$
$y = - 6$

#### Explanation:

You can solve the first equation for $y$ and obtain $y = - 3 x$. This literally means that $y$ and $- 3 x$ are the exact same thing, which in turn means that we can substitute one with the other, without changing the "meaning" of an equation.

So, let's do it in the second: instead of $y$, we will write $- 3 x$. The equation becomes

$5 x - 3 x = 4$

We can sum the terms in the left hand side to get

$2 x = 4$

And finally solve for $x$ dividing both sides by $2$:

$x = 2$

Now that we know that $x = 2$, we remember that $y$ and $- 3 x$ are the same thing. But again, since $x = 2$, $- 3 x = \left(- 3\right) \cdot 2 = - 6$

Jun 17, 2018

$\left(x , y\right) \to \left(2 , - 6\right)$

#### Explanation:

$3 x + y = 0 \to \left(1\right)$

$5 x + y = 4 \to \left(2\right)$

$\text{from equation } \left(1\right) \textcolor{w h i t e}{x} y = - 3 x \to \left(3\right)$

$\text{substitute "y=-3x" into equation } \left(2\right)$

$5 x - 3 x = 4 \Rightarrow 2 x = 4 \Rightarrow x = 2$

$\text{substitute "x=2" into equation } \left(3\right)$

$y = - 3 \times 2 = - 6$

$\text{point of intersection } = \left(2 , - 6\right)$
graph{(y+3x)(y+5x-4)=0 [-16.02, 16.02, -8, 8.02]}

Jun 17, 2018

$x = 2 \mathmr{and} y = - 6$

#### Explanation:

Let ,

$3 x + y = 0. . . \to \left(1\right)$

$5 x + y = 4. . . \to \left(2\right)$

From $\left(1\right)$ ,

$y = - 3 x \ldots \to \left(3\right)$

Subst .$y = - 3 x$ into $\left(2\right)$

$5 x + \left(- 3 x\right) = 4$

$\implies 2 x = 4$

=>color(blue)(x=2

From $\left(3\right)$ ,we get

$y = - 3 \left(2\right)$

=>color(blue)(y=-6

Hence,

$x = 2 \mathmr{and} y = - 6$