Question

HELP ! PLEASE

examine the system of equations.

Answer 1

The solution is
`(x=(-7)/(2),\ y=(-13)/(2) )`.

Solution:

Given system of equations are

`-3 x+y=4` ---------- (1)

`-9 x+5 y=-1` ---------- (2)

To solve the given system of equations by substitution method.

Let us take the equation (1) and find the value of y.

(1) ⇒
`-3 x+y=4`

Add 3x on both sides of the equation, we get

⇒
`y=4+3x`

Substitute y = 4 + 3x in equation (2), we get

`-9 x+5 (4+3x)=-1`

`-9 x+20+15x=-1`

Combine like terms together.

`-9 x+15x=-1-20`

`6x=-21`

Divide by 6 on both sides of the equation.

`$x=-(21)/(6)`

Divide the numerator and denominator by the common factor 3.

`$x=-(21/3)/(6/3)`

`$x=-(7)/(2)`

Now, substitute x value in y = 4 + 3x, we get

`$y=4+3\left((-7)/(2) \right)`

`$y=4+\left((-21)/(2) \right)`

Take LCM of the denominators and make the same.

`$y=(8)/(2) +(-21)/(2)`

`$y=(-13)/(2)`

Hence the solution is
`(x=(-7)/(2),\ y=(-13)/(2) )`.