Question

X+ 4y=8 and 3x+4y=0 determine the soulution

Answer 1

(-4,3)

Explanation:

Converting to slope-intercept form each:

• x + 4y = 8
• 3x + 4y = 0

x + 4y = 8

Shift 'x' term to the right side:

4y = -1x + 8

Now, divide right with the coefficient of y:

y = (-1x + 8)/4

y = (-1/4)x (+ 8/4)

Slope Intercept Form

y = -0.25x + 2

3x + 4y = 0

Shift 'x' term to the right side:

4y = -3x + 0

Now, divide right with the coefficient of y:

y = (-3x + 0)/4

y = (-3/4)x (+ 0/4)

Slope Intercept Form

y = -0.75x + 0

Now to solve for the system of:

• y = -0.25x + 2
• y = -0.75x + 0

Solve using substitution method.

The substitution method is a way to simplify using the expression of a singular variable in terms of another, thus removing the variable from the equation.

1) Solve y = -0.25+2 for y.

`y=-0.25x+2`

`y=-0.25x+2.0` (Simplify)

`y{+(-y)}=-0.25x+2+(-y)` ( Add (-y) on both sides)

`0=2.0-0.25x-y`

`0=2.0-0.25x-y` (Simplify)

`0{+(y)}=2.0-0.25x-y+(y)` ( Add (y) on both Sides )

`y=-0.25x+2.0`

`(y)/(1) =(-0.25x+2.0)/(1)` (Divide through by 1)

`y=-0.25x+2.0`

2) Substitute
`-0.25x+2.0` for y in y = -0.75x+0, then solve for x.

`{(-0.25\cdot x+2.0)}=-0.75x+0`

`-0.25x+2.0=-0.75x` (Simplify)

`-0.25x+2.0{+(-2.0)}=-0.75x+(-2.0)` (Add (-2.0) on both sides)

`-0.25x=-0.75x-2.0`

`-0.25x=-0.75x-2.0` (Simplify)

`-0.25x{+(0.75x)}=-0.75x-2.0+(0.75x)` (Add (0.75x) on both sides)

`0.5x=-2.0`

`(0.5x)/(0.5) =(-2.0)/(0.5)` ( Divide through by 0.5 )

`x=-4.0`

3) Substitute -4.0 for x in y = -0.25x + 2.0.

`y=-0.25x+2.0`

`y=1.0+2.0`

`y=3.0`

Answer

`x=-4.0{\text{ And }y=3.0`