# How do you solve y=2/7x+2, 6x-21y=-42?

Jun 21, 2018

There are infinite solutions.

#### Explanation:

The first equation already gives an expression for $y$ in terms of $x$. We can use this expression in the second equation to get

$6 x - 21 \left(\frac{2}{7} x + 2\right) = - 42$

Expand the left hand side:

$6 x - 6 x - 42 = - 42$

This leads to an equation like $0 = 0$, which means that the system is undetermined: there are infinite values of $x$ and $y$ would solve this system, as long as they are in the relation

$y = \frac{2}{7} x + 2$

In general, a linear system is composed by the equations of two lines, and we're looking for the point of intersection. In cases like this, both equations represent the same line, so there are infinite points of intersection.

Jun 21, 2018

$\text{Both the equations are same. Hence will have infinite solutions.}$

#### Explanation:

$y = \left(\frac{2}{7}\right) x + 2$

$7 y = 2 x + 14$

$- 2 x + 7 y = 14 , \text{ Eqn (1)}$

6x - 21y = -42, " Eqn (2)

As may be seen, both the equations are same. Hence will have infinite solutions.