We have the next system of equations
[tex]\begin{cases}y=0.5x+5\ldots(1) \\ x-2y=8\ldots(2)\end{cases}[/tex]To solve the systme we must replace equation (1) in equation (2)
[tex]x-2(0.5x+5)=8[/tex]Simplifying,
[tex]\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}[/tex]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.
