Respuesta :
Answer:
The point of intersection of the lines is [tex](2,6)[/tex].
Thus, Ariyonne's claim is incorrect.
Step-by-step explanation:
Given equations:
1) [tex]y=4x-2[/tex]
2) [tex]y=\frac{1}{2}x+5[/tex]
To find the point of intersection, we need to solve the given system of equations.
In order to solve the system we will use substitution method.
We will substitute value of [tex]y[/tex] from first equation in the second equation and solve for [tex]x[/tex]
So, we have
[tex]4x-2=\frac{1}{2}x+5[/tex]
Multiplying both sides by 2 to remove fraction.
[tex]2\times(4x-2)=2\times(\frac{1}{2}x+5)[/tex]
Using distribution.
[tex]8x-4=x+10[/tex]
Subtracting both sides by [tex]x[/tex]
[tex]8x-4-x=x+10-x[/tex]
[tex]7x-4=10[/tex]
Adding 4 to both sides.
[tex]7x-4+4=10+4[/tex]
[tex]7x=14[/tex]
Dividing both sides by 7.
[tex]\frac{7x}{7}=\frac{14}{7}[/tex]
[tex]x=2[/tex]
We can find value of [tex]y[/tex] by plugging in [tex]x=2[/tex] in the first equation.
[tex]y=4(2)-2[/tex]
[tex]y=8-2[/tex]
[tex]y=6[/tex]
So, the point of intersection of the lines is [tex](2,6)[/tex].
Thus, Ariyonne's claim is incorrect.
