Question

25 POINTS!!!!What are the solutions to the following system of equations?

y= x^2+3x-7
3x-y= -2

Answer 1

(x, y) = (3,11), (-3, -7)

Explanation:

Rearranging the linear equation we get y = 3x + 2

Now subbing this into the first eq we get 3x + 2 = x² + 3x - 7 which simplifies to x² = 9, so x = ±3 and hence y = 11 or -7

Answer 2

Given equations:

1. y = x^2 + 3x - 7 ...........(i)

2. 3x - y = -2 ...............(ii)

Substitute equation (i) into equation (ii):

3x - (x^2 + 3x - 7) = -2

Now, simplify the equation:

3x - x^2 - 3x + 7 = -2

Combine like terms:

-x^2 + 7 = -2

Move constant term to the right side:

-x^2 = -2 - 7

-x^2 = -9

Now, multiply both sides by -1 to make x^2 positive:

x^2 = 9

Now, take the square root of both sides:

x = ±√9

x = ±3

➡ Now that we have the values of x, we can find the corresponding values of y using equation (i):

For x = 3:

y = 3^2 + 3(3) - 7

y = 9 + 9 - 7

y = 11

For x = -3:

y = (-3)^2 + 3(-3) - 7

y = 9 - 9 - 7

y = -7

So, the solutions to the system of equations are (x, y) = (3, 11) and (x, y) = (-3, -7).