Question 1:
Solve the simultaneous equations x + 2y = 1 and 3x−2y=5.3x−2y=5.
Give you answer correct to three decimal places. [5 marks]
Solution:
x+2y=1x=1−2y ………… (1)3x−2y=5× xy, 3y−2x=5xy ………… (2)Substitute (1) into (2):3y−2(1−2y)=5y(1−2y)3y−2+4y=5y−10y210y2+2y−2=05y2+y−1=0a=5, b=1, c=−1y=−b±√b2−4ac2a=−1±√1−4(5)(−1)10
y=−1+√2110=0.3583=0.358 (3 dp)ory=−1−√2110=−0.5583=−0.558 (3 dp)From (1),When y=0.358x=1−2(0.3583) =0.283When y=−0.558x=1−2(−0.5583) =2.117
Solve the simultaneous equations x + 2y = 1 and 3x−2y=5.3x−2y=5.
Give you answer correct to three decimal places. [5 marks]
Solution:
x+2y=1x=1−2y ………… (1)3x−2y=5× xy, 3y−2x=5xy ………… (2)Substitute (1) into (2):3y−2(1−2y)=5y(1−2y)3y−2+4y=5y−10y210y2+2y−2=05y2+y−1=0a=5, b=1, c=−1y=−b±√b2−4ac2a=−1±√1−4(5)(−1)10
y=−1+√2110=0.3583=0.358 (3 dp)ory=−1−√2110=−0.5583=−0.558 (3 dp)From (1),When y=0.358x=1−2(0.3583) =0.283When y=−0.558x=1−2(−0.5583) =2.117