Systems of Equations

Question 9: Solve the simultaneous equations: 2 (x – y) = x + y – 1 = 2×2 – 11y2  [5 marks] Solution: 2 (x – y) = x + y – 1 2x – 2y = x + y – 1 x = 3y – 1 —- (1) x + y – 1 = 2×2 … Read more

Question 7: Solve the following simultaneous equations. 5y – 6x= 2 4 y x − 3 x y = 4. Solution: 5y – 6x= 2 —– (1) 4 y x − 3 x y = 4  ——- (2) From (1), y = 2 + 6 x 5 Substitute (3) into (2), 4 ( 2 + 6 x 5 … Read more

Question 5: Lisa has a rectangular plot of land. She plants orchid and rears fish in the areas as shown on diagram above. The area used for planting orchid is 460 m2 and the perimeter of the rectangular fish pond is 48 m. Find the value of x and y. Solution: Area used for planting … Read more

Question 3: Solve the following simultaneous equations. 3y – 2x= – 4 y2 + 4×2 = 2 Solution: 3y – 2x= – 4 —–(1) y2 + 4×2= 2 —–(2) From (1), y = 2 x − 4 3  ——- ( 3 ) Substitute (3) into (2), ( 2 x − 4 3 ) 2 + 4 x 2 = … Read more

Question 1: Solve the following simultaneous equations. y + 2 x = 2 2 x + 1 y = 5  Solution: y+2x=2−−−−(1) 2 x + 1 y =5−−−−(2) y=2−2x−−−−(3) substitute (3) into (2), 2 x + 1 2−2x =5 2( 2−2x )+x x( 2−2x ) =5 4−4x+x=5x( 2−2x ) 4−3x=10x−10 x 2 10 x 2 −13x+4=0 ( 5x−4 … Read more

Example 1: Solve the simultaneous equations. x + 1 4 y = 1  and  y 2 − 8 = 4 x . Solution: x + 1 4 y = 1 → ( 1 ) y 2 − 8 = 4 x → ( 2 ) x = 1 − 1 4 y → ( 3 … Read more

(A) Steps in solving simultaneous equations involving one linear equation and one non-linear equation: For the linear equation, arrange so that one of the unknown becomes the subject of the equation. Substitute the linear equation into the non-linear equation. Simplify and expressed the equation in the general form of quadratic equation a x 2 + … Read more