Question

Graph the systemY= 0.5 x + 5x - 2y=8find the solution to the system if there is no solution put no solution if there is infinite put infinitelable the system as consistent or inconsistent

Answer 1

We have the next system of equations

`\begin{cases}y=0.5x+5\ldots(1) \\ x-2y=8\ldots(2)\end{cases}`

To solve the systme we must replace equation (1) in equation (2)

`x-2(0.5x+5)=8`

Simplifying,

`\begin{gathered} x-\lbrack2(0.5x)+2(5)\rbrack=8 \\ x-\lbrack x+10\rbrack=8 \\ x-x-10=8 \\ -10=8\text{ } \\ \text{this, is false. So, the system has no solution} \end{gathered}`

To graph the system we must graph equation (1) and (2)

- equation (1)

x-intercept: (-10, 0)

y-intercept: (0, 5)

-equation (2)

x-intercept

The graphs never intersect, we can confirm that the system has no solution.