Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Solve the given system of equations.

4x-5y=10
-x-8=3y

Answer 1

Multiplying eqn no. two with 4 we add it up with eqn 1.

`4x - 5y = 10 \\ - 4x - 12y = 32 \\`

`- 17y = 42 \\ y = ( - 42)/(17)`

When

`- x - 8 = 3y \\ x + 3y = - 8`

`x = - 8 - 3 ( - 42)/(17 ) \\ x = - 8 + (42)/(17) \\ x = ( - 10)/(17)`

So, x = - 10/17 and y = - 42/17.

Answer 2

the value of x= -10/17 and y= -42/17

Explanation:

`4x-5y=10`

`-x-8=3y`

Use substitution method, solve the second equation for x

`-x-8=3y`

Add 8 on both sides

`-x=8+3y`, divide both sides by -1

`x=-8-3y`, now plug it in first equation

`4(-8-3y)-5y=10`

`-32-12y-5y=10`,combine like terms

`-32-17y=10`

Add 32 on both sides

`-17y= 42`

Divide by -17 on both sides

`y=(-42)/(17)`

Now plug in y in x =-8-3y and find out y

`x=-8-3((-42)/(17))=-8+(126)/(17) =-(10)/(17)`

the value of x= -10/17 and y= -42/17