Variable pairs determines the concept of an ordered pair and it shows you to plot ordered pairs on a graph. The variable determine the value of the particular terms of the equation.
The variable pair is a set of two variable like (x, y) written in parentheses. The variable in terms of graph represent the first value as x and the second value as y. (2,3) represents x axis is 2 units long and y axis is 3 units long.
Example Problem for Variable Pairs:
Solve for the ordered pair from the following equations:
4x + 3y = 12
2x + 3y = 8 solve for x and y
Solution:
Given that 4x + 3y = 12--------------------- (1)
2x + 3y = 8--------------------- (2)
Subtract the first equation and second equation,
4x + 3y = 12
2x + 3y = 8
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2x = 4
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That is
4x – 2x = 2x
3y – 3y = 0
12 – 8 = 4
Now we have the equation 2x = 4 after subtraction.
2x = 4
Divide by 2 on both sides
x = `4 / 2`
x = 2
Substitute the x = 2 in the first equation, we will get the value of y variable.
First equation 4x + 3y = 12
4(2) + 3y = 12
8 + 3y = 12
3y = 12 – 8
3y = 4
y = `4 / 3`
The solution is x = 2 and y = `4 /3` .
My forthcoming post is on Exponential Data Sets and Exponential Differentiation will give you more understanding about Algebra.
Example Problem for Variable Pairs:
Solve for the ordered pair from the following equations:
8x + 2y = 4
x + 3y = 5
Solution:
Given that 8x + 2y = 4--------------------- (1)
x + 3y = 5--------------------- (2)
Subtract the first equation and second equation,
3 * (1) 24x + 6y = 12
2 * (2) 2x + 6y =-10
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22x = 22
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That is
24x – 2x = 22x
6y – 6y = 0
12 – (-10) = 22
Now we have the equation 22x = 22 after subtraction.
Divide by 22 on both sides. we get
x = 1
Substitute the x = 22 in the first equation,
First equation 8x + 3y = 4
8(22) + 3y = 4
176 + 3y = 4
3y = 4 – 176
3y = -172
y = `-172 / 3`
The solution is x = 1 and y = -`172 /3` .
The value of variable pairs (x,y) is (1,-`172/3` )
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