Systems of Equations
Solve for X and Y
X + Y=6, 2X + Y = 8
7X + 3Y = 14, 5X + 9Y = 10
4X + Y = 16, 2X + 3Y = 24
Y = 25, 8X - 2Y = 14
Using the elimination method for solving simultaneous equations we get
X + Y=6, 2X + Y = 8
X + Y = 6 -- ( [1]
2X + Y = 8 -- ( [2]
( (Changing signs)
Substituting X = 2 in [1] we get
+ y = 6
y = 6 -- 2
y = 4
Therefore x = 2 and y = 4
X and y values thus found can be verified by substituting them in any one of the given equations.
2X + Y = 8
L.H.S = R.H.S
7X + 3Y = 14, 5X + 9Y = 10
7X + 3Y = 14 -- ((1)
5X + 9Y = 10 -- >(2)
Multiplying (1) by 5, we get
35x + 15y = 70 -- ( (3)
Multiplying (2) by 7, we get
35x + 63y = 70 -- ( (4)
(3)- (4),we get
-48y = 0
y = 0
Substituting y = 0 in [1] we get
7x +...
4X + Y = 16, 2X + 3Y = 24
4X + Y = 16 -- ((1)
2X + 3Y = 24 -- ((2)
Multiplying (1) by 3, we get
12X + 3Y = 48 -- ((3)
(3)-(2), we get
10x = 24
=> x = 2.4
Substituting x = 2.4 in (1) we get
4(2.4) + y = 16
9.6 + y = 16
=> y = 16 -- 9.6
=> y = 6.4
The values are
X = 2.4, y = 6.4
Verification:-
Substituting x = 2.4,y = 6.4 in (2) we get
2(2.4) + 3(6.4) = 24
4.8 + 19.2 = 24
L.H.S = R.H.S
d. 12X + Y = 25, 8X - 2Y = 14
12X + Y = 25 -- ((1)
8X - 2Y = 14 -- ((2)
Multiplying (1) by 2, we get
24x + 2y =…
Bibliography
1)Matthew Pinkey, "Simultaneous Equations,"
Accessed on March 16th 2005,
http://www.mathsrevision.net/gcse/pages.php?page=3
2) Blacksacademy, "Simultaneous Equations in Three Unknowns,"
http://www.blacksacademy.co.uk/data/MAQAST11.pdf
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