Question 1 (vii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
10x+y+2x−y=4
15x+y−5x−y=−2
10x+y+2x−y=4
15x+y−5x−y=−2
10x+y+2x−y=4
15x+y−5x−y=−2
Putting 1x+y=p and 1x−y=q in the given equations, we get;
10p+2q=4
⇒10p+2q−4=0...(i)
15p−5q=−2
⇒15p−5q+2=0...(ii)
Using cross multiplication, we get
p4−20=q−60−(20)=1−50−30
p−16=q−80=1−80
p−16=1−80 and q−80=1−80
p=15 and q=1
p=1x+y=15 and q=1x−y=1
x+y=5...(iii) and x−y=1...(iv)
Adding equation (iii) and (iv), we get
2x=6⇒x=3
Putting x = 3 in (iii), we get
3+y=5⇒y=2
Hence, x = 3 and y = 2