Solve this system of equations.

Answer:

(8,0)

Step-by-step explanation:

y= 0.50x - 4

y= -0.25x + 2

I changed it to make it:

0.25x + y = 2

-0.50x + y = -4

--

We subtract the y's and every equation to cancel out the y.

0.25x - (-0.50x) = 0.75x

2-(-4)=6

0.75x = 6

x = 8.

Plug the x into either equation. We'll do the first eqn.

0.25(8)+y=2

2 = y = 2

y = 0.

(8,0).

Answer:

x = 8, y = 0

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=\dfrac{1}{2}x-4&\\y=-\dfrac{1}{4}x+2\end{cases}[/tex]

First, substitute the first equation into the second:

[tex]\implies \dfrac{1}{2}x-4=-\dfrac{1}{4}x+2[/tex]

SOLVE FOR X.

Step 1: Multiply both sides by [tex]4[/tex] and simplify.

[tex]\\\implies 4\left(\dfrac{1}{2}x\right)-4(4)&=4\left(-\dfrac{1}{4}x\right)+2(4)\\\\\implies \dfrac{4}{2}x-16=-\dfrac{4}{4}x+8\\\\\implies 2x-16=-x+8[/tex]

Step 2: Add (1)[tex]x[/tex] to both sides.

[tex]\\\implies 2x + x-16=-x+x+8\\\\\implies 3x-16=8[/tex]

Step 3: Add [tex]16[/tex] to both sides.

[tex]\\\implies3x-16+16=8+16\\\\\implies 3x=24[/tex]

Step 4: Divide both sides by [tex]3[/tex].

[tex]\\\implies \dfrac{3x}{3}=\dfrac{24}{3}\\\\\implies \boxed{x=8}[/tex]

SOLVE FOR Y.

Step 1: Substitute [tex]8[/tex] as the value of [tex]x[/tex] in any of the given equations.

[tex]\\\implies y=\dfrac{1}{2}(8)-4[/tex]

Step 2: Simplify.

[tex]\\\implies y=4-4\\\\\implies \boxed{y=0}[/tex]

The solution to this system of equations is (8,0).

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