Question

Ariyonne claims (3,6) that is the point of intersection of the lines y=4x-2 and y=1/2x+5 Is she correct? How do you know?

Answer 1

Answer:

The point of intersection of the lines is  $(2,6)$.

Thus, Ariyonne's claim is incorrect.

Step-by-step explanation:

Given equations:

1) $y=4x-2$

2) $y=\frac{1}{2}x+5$

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 $y$ from first equation in the second equation and solve for $x$

So, we have

$4x-2=\frac{1}{2}x+5$

Multiplying both sides by 2 to remove fraction.

$2\times(4x-2)=2\times(\frac{1}{2}x+5)$

Using distribution.

$8x-4=x+10$

Subtracting both sides by $x$

$8x-4-x=x+10-x$

$7x-4=10$

Adding 4 to both sides.

$7x-4+4=10+4$

$7x=14$

Dividing both sides by 7.

$\frac{7x}{7}=\frac{14}{7}$

$x=2$

We can find value of $y$ by plugging in $x=2$ in the first equation.

$y=4(2)-2$

$y=8-2$

$y=6$

So, the point of intersection of the lines is  $(2,6)$.

Thus, Ariyonne's claim is incorrect.