# How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x-2y= 10 and -6x +4y= -20?

Oct 23, 2015

See the explanation.

#### Explanation:

$3 x - 2 y = 10$
$- 6 x + 4 y = - 20 | : \left(- 2\right)$

$3 x - 2 y = 10$
$3 x - 2 y = 10$

So, we get system of two equal equations and because of that, it has many solutions.

Let's pick one unknown as a parameter: $x = K$, then:

$3 K - 2 y = 10 \implies 2 y = 3 K - 10 \implies y = \frac{3 K - 10}{2} = \frac{3}{2} K - 5$

Every pair $\left(K , \frac{3}{2} K - 5\right)$ where $K \in R$ is solution of given system.