How do you solve the following linear system: 2x+y=-3/2, 6x+3y=5?

2 Answers
Mar 13, 2018

There is no solution for the pair of equations.

Explanation:

$2 x + y = - \frac{3}{2}$

Multiply 3 both sides

$\implies 3 \left(2 x + y\right) = 3 \times - \frac{3}{2}$

$\implies 6 x + 3 y = - \frac{9}{2}$

And , $6 x + 3 y = 5$

You see the LHS of both the equations are equal but the RHS of both the equations are unequal.

Thus , no solution exists for the given pair of linear equations.

Mar 13, 2018

$\text{no solution}$

Explanation:

$2 x + y = - \frac{3}{2} \to \left(1\right)$

$6 x + 3 y = 5 \to \left(2\right)$

$\text{From equation "(1)" we obtain}$

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

$\textcolor{b l u e}{\text{Substitute "y=-3/2-2x" into equation }} \left(2\right)$

$6 x + 3 \left(- \frac{3}{2} - 2 x\right) = 5$

$\Rightarrow \cancel{6 x} - \frac{9}{2} \cancel{- 6 x} = 5$

$\Rightarrow - \frac{9}{2} = 5$

$\text{Obviously this is not a true statement hence no solution}$

$\text{Consider the equations in "color(blue)"slope-intercept form}$

$\left(1\right) \to y = - \frac{3}{2} - 2 x$

$\left(2\right) \to y = - 2 x + \frac{5}{3}$

$\text{both lines have "m=-2rArr" parallel lines}$

$\text{thus they never intersect and so have no solution}$
graph{(y+2x+3/2)(y+2x-5/3)=0 [-10, 10, -5, 5]}