Complete the order pairs so each is a solution for the given equation
3x + 4y = 12
these are the numbers
( ,3) ( ,3/4) ( ,0) and (8/3, )
need to fill in the missing numbers
#3 ( ,0).
3x + 4y = 12. The problem is asking for the x value when y is .
3x + 4*0 = 12
3x + 0 = 12
3x = 12
x = 4
The others are done the same way. Fractions make it a little more difficult but generally the fraction can be modified by multiplying the equation through by the denominator.
To complete the ordered pairs so that they are solutions for the equation 3x + 4y = 12, we need to find the missing numbers.
Let's go one pair at a time:
1) ( , 3):
In this ordered pair, we want to find the value of x when y = 3.
Substitute y = 3 into the equation: 3x + 4(3) = 12
Simplify: 3x + 12 = 12
Subtract 12 from both sides: 3x = 0
Divide both sides by 3: x = 0
So, the ordered pair is (0, 3).
2) ( , 3/4):
In this ordered pair, we want to find the value of x when y = 3/4.
Substitute y = 3/4 into the equation: 3x + 4(3/4) = 12
Simplify: 3x + 3 = 12
Subtract 3 from both sides: 3x = 9
Divide both sides by 3: x = 3
So, the ordered pair is (3, 3/4).
3) ( , 0):
In this ordered pair, we want to find the value of x when y = 0.
Substitute y = 0 into the equation: 3x + 4(0) = 12
Simplify: 3x = 12
Divide both sides by 3: x = 4
So, the ordered pair is (4, 0).
4) (8/3, ):
In this ordered pair, we want to find the value of y when x = 8/3.
Substitute x = 8/3 into the equation: 3(8/3) + 4y = 12
Simplify: 8 + 4y = 12
Subtract 8 from both sides: 4y = 4
Divide both sides by 4: y = 1
So, the ordered pair is (8/3, 1).
In summary, the completed ordered pairs that are solutions for the equation 3x + 4y = 12 are:
(0, 3), (3, 3/4), (4, 0), and (8/3, 1).