Answer:
The values of [tex]m_{2}[/tex] and [tex]b_{2}[/tex] that will create a system of linear equations with no solution are [tex]m_{2} = -3[/tex] and [tex]b_{2} = -3[/tex].
Step-by-step explanation:
An example of a system of linear equations are two lines parallel to each other. In other words, there are two lines such that:
[tex]y = m_{1}\cdot x + b_{1}[/tex] (1)
[tex]y = m_{2}\cdot x + b_{2}[/tex] (2)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m_{1}[/tex], [tex]m_{2}[/tex] - Slope.
[tex]b_{1}[/tex], [tex]b_{2}[/tex] - y-Intercept.
If both lines are parallel to each other, then we must observe these two conditions:
1) [tex]m_{1} = m_{2}[/tex]
2) [tex]b_{1} \ne b_{2}[/tex]
Therefore, the values of [tex]m_{2}[/tex] and [tex]b_{2}[/tex] that will create a system of linear equations with no solution are [tex]m_{2} = -3[/tex] and [tex]b_{2} = -3[/tex].
