To solve an equation on the form ax^2+bx+c=0, use the Quadratic Formula.
(- 2, - 2)
Practice makes perfect
We will solve the given system of equations using the Substitution Method.
x-2y=2 & (I) y^2-x^2=2x+4 & (II)
Note that neither of the variables is isolated in either equation, so we need to start by isolating x in Equation (I).
x-2y=2 y^2-x^2=2x+4 ⇔ x=2+2y y^2-x^2=2x+4
The x-variable is isolated in Equation (I). This allows us to substitute its value 2+2y for x in Equation (II).
Notice that in Equation (II), we have a quadratic equation in terms of only the y-variable.
- 3y^2-12y-12=0 ⇔ - 3y^2+( - 12)y+( - 12)=0
We can substitute a= - 3, b= - 12, and c= - 12 into the Quadratic Formula.
We found that x=- 2 when y=- 2. Thus, the solution of the system is (- 2,- 2).
Checking Our Answer
Checking the answer
We can check our answer by substituting the solution into both equations. If it produce true statements, our solution is correct. We will substitute -2 for x and -2 for y in Equation (I) and Equation (II).
