Question

Solve the system of equations

Answer 1

To find the points of intersection between the two equations, we need to set them equal to each other and solve for the x-coordinate(s) of the intersection point(s).

Given the equations:

1. y = 3x

2. y = x^2 - 4

Setting them equal to each other:

3x = x^2 - 4

Now, we need to solve this quadratic equation for x.

x^2 - 3x - 4 = 0

To factor the equation:

(x - 4)(x + 1) = 0

Setting each factor to zero and solving for x:

x - 4 = 0 -> x = 4

x + 1 = 0 -> x = -1

Now that we have the x-coordinates of the intersection points, we can find the corresponding y-coordinates using either of the original equations. Let's use the first equation, y = 3x:

For x = -1:

y = 3(-1) = -3

For x = 4:

y = 3(4) = 12

So, the points of intersection are (-1, -3) and (4, 12).

The correct answer is option B: (-1, -3) and (4, 12).

Explanation:

Answer 2

B. (-1,-3) and (4,12)

Explanation:

Given equation:

`\sf y = 3x\\\sf y = x^2 -4`

We can solve this by substituting the value of y in the second equation.

`\sf 3x = x^2 -4`

keep the terms on one side, we get

`\sf x^2 -4 -3x=0\\\sf x^2-3x-4 =0`

we can factor it by middle-term factorization:

`\sf x^2 -(4-1)x-4 =0\\\sf x^2 -4x + x -4 =0`

Taking common from each two terms

`\sf x(x-4) +1(x-4) =0\\\sf (x-4)(x+1)=0`

Either

x = 4

or

x = -1

Again,

We can substitute the value of x in the first equation, and we get

when x =4

y =3*4 =12

Therefore, one point is (4,12)

when x = -1

y =3*-1 =-3

Therefore, another point is (-1,-3)

Therefore, The answer is B. (-1,-3) and (4,12)