CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS 9.3
For example the solutionof
y− 2 x =− 4 (9.2)
x^2 + y = 4 (9.3)is:
In (9.2)
y = 2x− 4 (9.4)Substitute (9.4) into (9.3):
x^2 + (2x− 4) = 4
x^2 + 2x− 8 = 0Factorise to get:
(x + 4)(x− 2) = 0
∴ x =− 4 and x = 2Substitute the values of x into (9.4) to find y:
y = 2(−4)− 4 y = 2(2)− 4
y =− 12 y = 0
(−4;−12) (2;0)As expected, these solutions are identical to those obtained by the graphical solution.
Example 2: Simultaneous Equations
QUESTIONSolve algebraically:y− x^2 + 9 = 0 (9.5)
y + 3x− 9 = 0 (9.6)SOLUTIONStep 1 : Make y the subject of the linear equation
In (9.5):y + 3x− 9 = 0
y =− 3 x + 9 (9.7)Step 2 : Substitute into the quadratic equation