Question

What is the solution to this system of equations? 10 y=x-4 y = -0.5x + 8 2 2 8 10 O A. (4,8) O B. (4,2) O C. (2,4) O D. (8,4) HELPPPPP

Answer 1

the given system of equations :

`\begin{gathered} 10y\text{ = x -4} \\ y\text{ =-0.5x+8} \end{gathered}`

we can solve this equations by using substitution method :

Simplify the equation (2) for y and substitute the value of y in equation (1)

`\begin{gathered} y\text{ =-0.5x +8} \\ \text{The equation already shows the solution for the y} \\ \text{Substitute it to the first equation} \\ y=x-4 \\ (-0.5x+8)=x-4 \\ -0.5x+8=x-4 \\ \text{ x+0.5x=8+4} \\ 1.5x=12 \\ x=8 \end{gathered}`

x = 8

now, put x = 8 in the second equation and solve for y

`\begin{gathered} y=-0.5x+8 \\ y=-0.5(8)+8 \\ y=-4+8 \\ y=4 \end{gathered}`

y = 4

Answer : D (x,y) = (8, 4)