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Sagot :
Given:
Some equations are given as below
(i) -5x + 3y = 51
y = 10x - 8
(ii) 6x + y = -10
5x + y = -10
(iii) 2x - y = 32
y - 5x = 13
(iv) 3x -y = 7
x - 2y = 4
Find:
we have to solve these equations.
Explanation:
(i) -5x + 3y = 51 ....................(1)
y = 10x - 8........................(2)
put y = 10x - 8 in eqn (1), we get
-5x + 3(10x - 8) = 51
-5x + 30x - 24 = 51
25x = 51 + 24
25x = 75
x = 75/25
x = 3
put x = 3 in eqn (2), we get
y = 10(3) - 8 = 30 - 8 = 22
Therefore, x = 3 and y = 22
answer is (3, 22)
...................................................................................................
(ii) 6x + y = -10........................(3)
5x + y = -10..........................(4)
subtract eqn(4) from eqn(3), we get
6x - 5x = 0
x = 0
put x = 0 in eqn(3). we get
6(0) + y = -10
y = -10
Therefore, x = 0, y = -10
Answer is (0, -10)
.................................................................................................
(iii) 2x - y = 32........................(5)
y - 5x = 13..........................(6)
add eqn(5) and eqn(6), we get
2x -y + y - 5x = 32 + 13
-3x = 45
x = -45/3
x = -15
put x = -15 in eqn(5), we get
2(-15) - y = 32
-30 - y = 32
-y = 32 + 30
y = -62
Therefore, x = -15. y = -62
Answer is (-15, -62)
.........................................................................................................
(iv) 3x -y = 7..............................(7)
x - 2y = 4.............................(8)
Multiply eqn(8) by 3 and subtract from eqn (7) as following
3x - y = 7
3x - 6y = 12
- + -
.....................
5y = -5
y = -1
put y = -1 in eqn(7), we get
3x - (-1) = 7
3x + 1 = 7
3x = 7 - 1
3x = 6
x = 6/3
x = 2
Therefore, x = 2 and y = -1
Answer is (-1, 2)
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