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Vladimir79 [104]
3 years ago
8

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?

Mathematics
1 answer:
yan [13]3 years ago
3 0

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.

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