Q.1) Complete the following activity to solve the simultaneous equations.
5x + 3y = 9
2x - 3y = 12
7x - 0 = 21
x = 21
7
x = 3
Putting the value of x = 3 in equation (1) we get
5x + 3y = 9------(1)
5(3) + 3y = 9
15 + 3y = 9
3y = 9 - 15
3y = -6
y = -6
3
y = -2
Thus, (x,y) = (3,-2)
Q.2) Solve the following simultaneous equation.
3a + 5b = 26
a + 5b = 22
SOLUTION :-
3a + 5b = 26-----(1)
a + 5b = 22-------(2)
Subtracting (2) from (1)
3a + 5b = 26
a + 5b = 22
2a = 4
a = 4/2
a = 2
Putting the value of a = 2 in eq (2)
a + 5b = 22-----(2)
2 + 5b = 22
5b = 22 - 2
5b = 20
b = 20/5
b = 4
Thus, (a,b) = (2,4)
Q.3) Solve the following simultaneous equation.
x + 7y = 10
3x - 2y = 7
SOLUTION :-
x + 7y = 10-----(1)
3x - 2y = 7------(2)
Multiply equation (1) by 3,
3x + 21y = 30-----(3)
Subtracting eq (2) from (3) ,we get,
3x + 21y = 30
3x - 2y = 7
0 + 23y = 23
23y = 23
y = 23/23
y = 1
Putting the value of y = 1 in eq (2), we get,
3x - 2y = 7
3x -2(1) = 7
3x - 2 = 7
3x = 7 + 2
3x = 9
x = 9/3
x = 3
Thus, (x,y) = (3,1).
Q.4) Solve the following simultaneous equation.
2x - 3y = 9
2x + y = 13
SOLUTION :-
2x - 3y = 9------(1)
2x + y = 13-----(2)
Subtracting eq (1) from (2) ,we get,
2x - 3y = 9
2x + y = 13
0 - 4y = -4
-4y = -4
y = -4/-4
y = 1
Substitute y = 1 in eq (2)
2x + y = 13
2x + 1 = 13
2x = 13 - 1
2x = 12
x = 12/2
x = 6
Thus, (x,y) = (6,1).
Q.5) Solve the following simultaneous equation.
5m - 3n = 19
m - 6n = -7
SOLUTION :-
5m - 3n = 19----(1)
m - 6n = -7------(2)
Multiply eq (1) by 2, we get,
10m - 6n = 38----(3)
Subtracting eq (2) from (3) ,we get,
10m - 6n = 38
m - 6n = -7
9m = 45
m = 45/9
m = 5
Putting the value of m = 5 in eq (2), we get,
m - 6n = -7
5 - 6n = -7
-6n = -7 - 5
-6n = -12
n = -12/-6
n = 2
Thus, (m,n) = (5, 2).
Q.6) Solve the following simultaneous equation.
5x + 2y = -3
x + 5y = 4
SOLUTION :-
5x + 2y = -3-----(1)
x + 5y = 4--------(2)
Multiply (2) with 5 we get,
5x + 25y = 20-----(3)
Subtracting eq (3) from (1) we get,
5x + 2y = -3
5x + 25y = 20
0 - 23y = -23
-23y = -23
y = -23/-23
y = 1
Putting the value of y = 1 in eq (2) we get,
x + 5y = 4
x + 5(1) = 4
x + 5 = 4
x = 4 - 5
x= -1
Thus, (x,y) = (-1, 1).
Q.7) Solve the following simultaneous equation.
1/3x + y =10/3
2x + 1/4y = 11/4
SOLUTION :-
1/3x + y = 10/3-----(1)
2x + 1/4y = 11/4---(2)
Multiply (1) with 3 & (2) with 4
x + 3y = 10----(3)
8x + y = 11----(4)
Multiply (4) with 3
24x + 3y = 33----(5)
Subtracting eq (5) from (3)
x + 3y = 10
24x + 3y = 3
- 23x = -23
x = -23/-23
x = 1
Putting the value of x = 1 in eq (3)
x + 3y = 10
1 + 3y = 10
3y = 10 - 1
3y = 9
y = 9/3
y = 3
Thus, (x,y) = (1, 3).
Q.7) Solve the following simultaneous equation.
99x + 101y = 499
101x + 99y = 501
SOLUTION :-
99x + 101y = 499----(1)
101x + 99y = 501----(2)
Adding (1) and (2)
200x + 200y = 1000---(3)
divide eq (3) with 200
x + y = 5-----(4)
Subtracting (1) from (2), we get,
2x - 2y = 2----(5)
divide eq (5) with 2
x - y = 1----(6)
Adding eq (4) & (6)
x + y = 5
x - y = 1
2x = 6
x = 6/2
x = 3
Putting the value of x = 3 in eq (6)
x - y = 1
3 - y = 1
y = 2
Thus, (x,y) = (3, 2).
Q.8) Solve the following simultaneous equation.
49x - 57y = 172
57x - 49y = 252
SOLUTION :-
49x - 57y = 172----(1)
57x - 49y = 252----(2)
Adding (1) and (2)
(49x + 57y) + (-57y-49) = 172 + 252
106x +(-106y) =424
106(x-y) =424
(x-y) = 424/106
x-y =4----(3)
Subtracting (2) from (1)
(57x - 49x) + [-49-(-57y)]=252-172
8x +(-49y+57y) = 80
8x + 8y =80
8(x+y) = 80
x + y = 80/8
x + y = 10----(4)
Adding (3) and (4)
x+x-y+y=4+10
2x =14
x= 7
putting the value of x = 7 in eq (4)
x +y =10
7+y=10
y=10-7
y=3
Thus, (x,y) = (7,3).
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