#### Grade 10 Mathematics - More Exercises.

1.
2.
x + y = 7 . . . (1)
x − y = 7 . . . (1)
2x + y = 11 . . . (2)
2x + y = 5 . . . (2)
(2) − (1):
x = 4
(1) + (2) :
3x = 12
Into (1):
4 + y = 7
x = 4
y = 7 − 4
Into (1):
4 − y = 7
y = 3
y = − 3
x = 4   and   y = 3
x = 4   and   y = − 3
3.
x + 2y = 11 . . . (1)
3x + y = 13 . . . (2)
4.
x − 2y = 3 . . . (1)
2x − y = 18 . . . (2)
(1) X 3:
3x − 6y = 33 . . . (3)
(2) X 2 :
4x − 2y = 36 . . . (3)
(3) − (2):
5y = 20
(3) − (1) :
3x = 33
y = 4
x = 11
Into (1):
x + 2(4) = 11
Into (2):
2(11) − y = 18
x = 11 − 8
− y = 18 − 22
x = 3
y = 4
x = 3   and   y = 4
x = 11   and   y = 4
5.
x = 5   and   y = − 1
6.
x = − 3   and   y = 6
7.
x = 3   and   y = 4
8.
x = 8   and   y = 10
9.
5x − y − 2 = 0
10.
3x − 2y − 3 = 5
5x − y = 2 . . . (1)
3x − 2y = 8 . . . (1)
11x − 2y = 6 . . . (2)
x + y = 6 . . . (2)
(1) X 2:
10x − 2y = 4 . . . (3)
(2) X 2:
2x + 2y = 12 . . . (3)
(2) − (3):
x = 2
(1) + (3) :
5x = 20
Into (1):
5(2) − y = 2
x = 4
− y = 2 − 10
Into (2):
4 + y = 6
y = 8
y = 2
x = 2   and   y = 8
x = 4   and   y = 2
11.
x = − 1   and   y = − 1,5
12.
x = 2   and   y = − 3
13.
2x − 3y = 22 . . . (1)
5x + 4y = 9   . . . (2)
14.
7x + 5y + 11 = 0
(1) X 4:
8x − 12y = 88 . . . (3)
7x + 5y = − 11 . . . (1)
2x − 9y + 14 = −10
(2) X 3:
15x + 12y = 27 . . . (4)
2x − 9y = − 24 . . . (2)
(3) + (4) :
23x = 115
(1) X 9:
63x + 45y = − 99 . . . (3)
x = 5
(2) X 5:
10x − 45y = − 120 . . . (4)
Into (2):
5(5) + 4y = 9
(3) + (4) :
73x = − 219
4y = − 16
x = − 3
y = − 4
Into (1):
7(− 3) + 5y = − 11
x = 5   and   y = − 4
5y = 10
y = 2
x = − 3   and   y = 2
15.
3x + 2y + 5 = 0
16.
8x − 5y − 57 = 0
3x + 2y = − 5 . . . (1)
8x − 5y = 57 . . . (2)
4x + 3y + 6 = 0
3x + 7y + 23 = 0
4x + 3y = − 6 . . . (2)
3x + 7y = − 23 . . . (2)
(1) X 3:
9x + 6y = − 15 . . . (3)
(1) X 7:
56x − 35y = 399 . . . (3)
(2) X 2:
8x + 6y = − 12 . . . (4)
(2) X 5:
15x + 35y = − 115 . . . (4)
(3) − (4):
x = − 3
(3) + (4):
71x = 284
Into (1):
3(− 3) + 2y = − 5
x = 4
2y = − 5 + 9
Into (2):
3(4) + 7y = − 23
y = 2
7y = − 23 − 12
x = − 3   and   y = 2
y = − 5
x = 4   and   y = − 5
17.
x = − 2   and   y = − 3
18.
x = 5   and   y = − 2
19.
10x + 2y = 17 . . . (1)
5x + 4y = 16 . . . (2)
20.
5x − 2y = 0,6 . . . (1)
2x + y = 3,3 . . . (2)
(1) X 2:
20x + 4y = 34 . . . (3)
(2) X 2:
4x + 2y = 6,6 . . . (3)
(3) − (2):
15x = 18
(1) + (3):
9x = 7,2
x = 1,2
x = 0,8
Into (1):
10(1,2) + 2y = 17
Into (2):
2(0,8) + y = 3,3
2y = 17 − 12
y = 3,3 − 1,6
y = 2,5
y = 1,7
x = 1,2   and   y = 2,5
x = 0,8   and   y = 1,7
21.
x = 0,4   and   y = − 0,6
22.
x = 1,2   and   y = 3,4
23.
x = 0,25   and   y = 0,5
24.
x = 1,5   and   y = 0,4