Question

y = x^2 +5x - 3

y - x = 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can substitute the expression for y from the first equation into the second equation.

From the first equation, we have y = x^2 + 5x - 3.

Substituting this into the second equation, we get:

(x^2 + 5x - 3) - x = 2

Expanding the equation, we have:

x^2 + 5x - 3 - x = 2

Combining like terms, we have:

x^2 + 4x - 3 = 2

Rearranging the equation, we get:

x^2 + 4x - 5 = 0

Now we can use the quadratic formula to solve for x:

x = (-4 ± √(4^2 - 4(1)(-5))) / 2(1)

x = (-4 ± √(16 + 20)) / 2

x = (-4 ± √(36)) / 2

x = (-4 ± 6) / 2

This gives us two possible solutions for x:

x = (-4 + 6) / 2 = 1

x = (-4 - 6) / 2 = -5

Now we can substitute these values of x back into the first equation to find the corresponding values of y.

For x = 1, we have:

y = (1)^2 + 5(1) - 3
y = 1 + 5 - 3
y = 3

So one solution to the system of equations is x = 1, y = 3.

For x = -5, we have:

y = (-5)^2 + 5(-5) - 3
y = 25 - 25 - 3
y = -3

So the other solution to the system of equations is x = -5, y = -3.