Question

Plz help

5 points////

Answer 1

There is a technique to solve system of equations called by comparison.
The given problem is a typical example of the situation
y=x^2...........................................(1)
y=7x.............................................(2)
The left hand side of each equation equals y, and the right hand sides do not contain y.
Therefore we can match the two right hand sides and solve for x.
x^2=7x
rearrange, and factor
x^2-7x=0
x(x-7)=0
=>
x=0 or x-7=0
=>
x=0 or 7

We can now proceed to find y by substituting value of x in (1)...y=x^2
x=0 => y=0^2=0
x=7=> y=7^2=49
Therefore
Answer: Solutions are (0,0) and (7,49)

Answer 2

Hey there!

To start, you know that y=x^2 and y=7x.

In knowing that the two expressions are set to the same value, y, you can set both equations equal to one another:
x^2=7x

Now, set the equation to 0 to solve for your solutions:
x^2=7x
x^2-7x=7x-7x
x^2-7x=0

Now, look for any common factors that can be factored out of the equation:
x^2-7x=0 (both have a common factor of x)
x(x-7)=

Notice that you have two factors: x and (x-7). This signifies that you have two values for x. To solve for the two values, set both factors to 0:
x=0
x-7=0

Since you have x=0, 0 would be one of the values of x.

Now, solve x-7=0 for the value of x:
x-7=0
x=7

Now that you have the value of x, 7 and 0, plug the values into any of the original equations to find the corresponding y values:
y=x^2
x=0

y=(0)^2
y=0

One solution set would be (0,0).

y=x^2
x=7

y=(7)^2
y=49

Another set would be (7,49).

Therefore, your final answer would be the second answer choice:
(0,0) and (7,49)

Hope this helps you out! :)