Good day my students, in this post i'll teach you how to solve simultaneous equations.Simultaneous equations is anther branch in mathematics that involved letters with numbers,
if you want to know how this kind of math can be solved, you must be familiar with (open sentences) that deals with missing numbers where a particular letter represent numbers, but here is about solution by the method of subtraction.
Some students get it hard to deal with simultaneous equation,here i will show the simple tricks.Consider x - y, this involve finding the value of x and y to balance both x and y.Beside, x - y can be equation ...1
Examples
a. x - y = 3 ....... (1)equation 1
2x - y =8 .......(2)equation 2
Now lets find the value of x and y that will balance the two sides...
x - y = 3 ....... (1)equation 1
2x - y =8 ........(2)equation 2
now we will express either x in terms of y or in terms of x from one of the two equations.
For x - y = 3 ,we have
x - y+y = 3 + y
x = 3 + y ......(3) equation (iii)
Subtract the value x in equation 2.
2(3 + y) - y =8
6 + 2y - y = 8
6 + y = 8 ..... (2y - y is 1y but do not include 1 because y is 1 , 1 x y = y)
y = 8 - 6
y = 2
Note: 6 + y = 8
subtract y from both sides
6 + y-y = 8 - y
6 = 8 - y
y = 8 - 6 = 2
Subtract for y = 2 in equa.3 (x = 3 + y)
x = 3 + y
= 3 + 2 ( do not forget that y is 2)
x = 5
x = 5 and y = 2
b. x - y = 7
2x + 3y = 15
Now lets find the value of x and y that will balance the two sides...
x - y = 7.......(1)equation 1
2x + 3y = 15 ........(2)equation 2
From x - y = 7, we have
x - y = 7
add +y to both sides
x - y + y= 7 + y
x = 7 + y ......(3) equation (iii)
Subtract the value x in equation 2.
2(7 + y) + 3y = 15 ----- 2(a) means 2xa = 2a then, 2(7) means 2 x 7 = 14
14 + 2y + 3y = 15 ----- 2 x 7 before 2 x y also 2y + 3y = 5y ( the same term)
14 + 5y = 15
5y = 15 - 14
5y - 1
y = 5 - 1
y = 4
Subtract for y = 4 in equa.3 (x = 7 + y)
x = 7 + y
= 7 + 4 (y is 4 )
x = 11
x = 11 and y = 4
You too, always find the value of y before x.
c. x - 2y = 1
2x + 3y = 5
Now lets find the value of x and y that will balance the two sides...
x - 2y = 1.......(1)equation 1
2x + 3y = 5 ........(2)equation 2
from x - 2y = 1 , we have
x - 2y + 2y = 1 + 2y
x = 1 + 2y .........3 equation 3
Subtract the value of x in equation 2.
2(1 + 2y) + 3y = 5
2 + 4y + 3y =5
2 + 7y = 5
7y = 5 - 2
7y = 3
y = 7 - 3
y = 4
Subtract for y = 4 in equa.3 (x = 1 + 2y)
x = 1 + 2y
= 1 + 2(4) do dot forget that y is 4
x = 1 + 8
x = 9
if y = 2 and you have, x = 2 + y, you do it this way, x = 2 + 9 = 11, because y = 9
Follow up my pattern an you're good to go, but be familiar with open sentences.
Solve the following simultaneous equations
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