Solve the system of equations.

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

1 answer

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

Substituting Y = x + 2 into the first equation, we get:

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

Rearranging the equation to set it equal to zero:

x^2 + 4x - 5 = 0

From there, we can factor the quadratic equation:

(x + 5)(x - 1) = 0

Setting each factor equal to zero:

x + 5 = 0 or x - 1 = 0

Solving for x, we have:

x = -5 or x = 1

Substituting these values back into either of the original equations, we can solve for Y.

When x = -5:

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

When x = 1:

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

Thus, the solution to the system of equations is x = -5, Y = -3 or x = 1, Y = 3.