Question

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

Answer 1

There is no solution for the pair of equations.

Explanation:

`2x+y=-3/2`

Multiply 3 both sides

`=> 3(2x+y)=3xx-3/2`

`=> 6x+3y = -9/2`

And , `6x+3y=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.

Answer 2

`"no solution"`

Explanation:

`2x+y=-3/2to(1)`

`6x+3y=5to(2)`

`"From equation "(1)" we obtain"`

`y=-3/2-2x`

`color(blue)"Substitute "y=-3/2-2x" into equation "(2)`

`6x+3(-3/2-2x)=5`

`rArrcancel(6x)-9/2cancel(-6x)=5`

`rArr-9/2=5`

`"Obviously this is not a true statement hence no solution"`

`"Consider the equations in "color(blue)"slope-intercept form"`

`(1)toy=-3/2-2x`

`(2)toy=-2x+5/3`

`"both lines have "m=-2rArr" parallel lines"`

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