Answer: Yes, at the 1st hour and 6th mile.
Step-by-step explanation:
If [tex]x=[/tex] The number of hours and [tex]y=[/tex] The number of miles, then the system of equations is [tex]\left \{ {{y=4x+2} \atop {y=6x}} \right.[/tex]where Micah is the first equation and Luke is the second.
Solve by Substitution:
1) Solve [tex]y=4x+2[/tex] for [tex]y[/tex]:
[tex]y=4x+2[/tex]
2) Substitute [tex]4x+2[/tex] for [tex]y[/tex] in [tex]y=6x[/tex]:
[tex]y=6x[/tex]
[tex]4x+2=6x[/tex]
3) Add -6x to both sides:
[tex]4x+2+-6x=6x+-6x[/tex]
4) Simplify both sides of the equation:
[tex]-2x+2=0[/tex]
5) Add -2 to both sides:
[tex]-2x+2+-2=0+-2[/tex]
6) Simplify both sides of the equation:
[tex]-2x=-2[/tex]
7) Divide both sides by -2:
[tex]\frac{-2x}{-2} =\frac{-2}{-2}[/tex]
8) Simplify both sides of the equation:
[tex]x=1[/tex]
9) Substitute [tex]1[/tex] for [tex]x[/tex] in [tex]y=4x+2[/tex]:
[tex]y=4x+2[/tex]
[tex]y=(4)(1)+2[/tex]
10) Simplify both sides of the equation:
[tex]y=6[/tex]
Therefore, They meet at the 1st hour at the 6th mile
Solve by elimination:
You can't solve the system of equations by elimination
Solve by graphing:
They cross at (1, 6), which supports my answer.
