0.2x+0.3y=1.3, 0.4x+0.5y=2.3
Answers
Explanation:
Given :-
0.2x+0.3y=1.3, 0.4x+0.5y=2.3
To find:-
Solve the given equations 0.2x+0.3y=1.3, 0.4x+0.5y=2.3
Solution:-
Method-1:-
Elimination method:-
Given equations are
0.2x+0.3y=1.3
On multiplying with 10 both sides then
2x + 3y = 13
On multiplying with 2 both sides
4x +6y = 26-------------(1)
0.4x+0.5y=2.3
On multiplying with 10 both sides then
4x + 5y = 23 ----------(2)
On Subtracting (2) from (1) then
4x + 6y = 26
4x + 5y = 23
(-)
___________
0+y = 3
___________
y= 3
From (1)
4x+6(3)= 26
=>4x+18 = 26
=>4x = 26-18
=>4x = 8
=>x=8/4
=>x=2
Solution =(2,3)
_______________________________
Method -2:-
Substitution method:-
Given equations are
0.2x+0.3y=1.3
On multiplying with 10 both sides then
2x + 3y = 13
=>2x = 13-3y
=>x = (13-3y)/2------(1)
and 0.4x+0.5y=2.3
On multiplying with 10 both sides then
4x + 5y = 23 ----------(2)
On Substituting the value of x in (2) then
=>4[(13-3y)/2] +5y = 23
=>2(13-3y)+5y = 23
=>26-6y+5y =23
=>26-y = 23
=>y=26-23
=>y =3
On Substituting the value of y in (1) then
=>x =[ (13-3(3)]/2
=>x = (13-9)/2
=>x = 4/2
=>x = 2
Solution = (2,3)
Answer:-
x=2
y=3
The solution for the given problem is (2,3)
Used methods :-
- Elimination method
- Substitution method
Check :-
If x=2 and y=3 then
LHS :-0.2x+0.3y
=>0.2(2)+0.3(3)
=>0.4+0.9
=>1.3
LHS = RHS
If x=2 and y=3 then
LHS :- 0.4x+0.5y
=>0.4(2)+0.5(3)
=>0.8+1.5
=>2.3
LHS = RHS
Verified the given relations
Answer:
Draw a line l and a point X on it. Through x, draw a line segment XY perpendicular to l.
Again, draw a perpendicular XY at Y. (Use ruler and compass only)