Tell whether the given ordered pair is a solution of each equation.
3x + 5 = y;(1, 8)
Y = -2 (x + 3 ); (-6,0)
Y= (x - 1.2) (-3); (0,1.2)
10 - 5x = y; (-4,10)
Describe the pattern in the table using words , an equation . Extend the pattern for x= 5,6,and 7
X: 1,2,3,4
Y: 15,25,35,45
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To determine if a given ordered pair is a solution to an equation, we substitute the values into the equation and check if it holds true.
1) For the equation 3x + 5 = y and the ordered pair (1, 8):
Substituting x = 1, we get 3(1) + 5 = 8, which is true.
Therefore, the ordered pair (1, 8) is a solution to the equation 3x + 5 = y.
2) For the equation y = -2(x + 3) and the ordered pair (-6, 0):
Substituting x = -6, we get y = -2(-6 + 3) = -2(-3) = 6, which is not equal to 0.
Therefore, the ordered pair (-6, 0) is not a solution to the equation y = -2(x + 3).
3) For the equation y = (x - 1.2)(-3) and the ordered pair (0, 1.2):
Substituting x = 0, we get y = (0 - 1.2)(-3) = (-1.2)(-3) = 3.6, which is equal to 1.2.
Therefore, the ordered pair (0, 1.2) is a solution to the equation y = (x - 1.2)(-3).
4) For the equation 10 - 5x = y and the ordered pair (-4, 10):
Substituting x = -4, we get 10 - 5(-4) = 10 + 20 = 30, which is not equal to 10.
Therefore, the ordered pair (-4, 10) is not a solution to the equation 10 - 5x = y.
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To describe the pattern in the given table and extend it for x = 5, 6, and 7:
The pattern in the table shows that the value of y is 10 times the value of x, plus 5.
Equation: y = 10x + 5
Using this equation, we can extend the pattern for x = 5, 6, and 7.
For x = 5: y = 10(5) + 5 = 55
For x = 6: y = 10(6) + 5 = 65
For x = 7: y = 10(7) + 5 = 75
To determine whether a given ordered pair is a solution of an equation, you need to substitute the values of x and y into the equation and check if it holds true.
1. For the equation 3x + 5 = y and the ordered pair (1, 8):
Substitute x = 1 and y = 8 into the equation:
3(1) + 5 = 8
3 + 5 = 8
8 = 8
The equation holds true, so (1, 8) is a solution of 3x + 5 = y.
2. For the equation y = -2(x + 3) and the ordered pair (-6, 0):
Substitute x = -6 and y = 0 into the equation:
0 = -2(-6 + 3)
0 = -2(-3)
0 = 6
The equation does not hold true, so (-6, 0) is not a solution of y = -2(x + 3).
3. For the equation y = (x - 1.2)(-3) and the ordered pair (0, 1.2):
Substitute x = 0 and y = 1.2 into the equation:
1.2 = (0 - 1.2)(-3)
1.2 = (-1.2)(-3)
1.2 = 3.6
The equation does not hold true, so (0, 1.2) is not a solution of y = (x - 1.2)(-3).
4. For the equation 10 - 5x = y and the ordered pair (-4, 10):
Substitute x = -4 and y = 10 into the equation:
10 = 10 - 5(-4)
10 = 10 + 20
10 = 30
The equation does not hold true, so (-4, 10) is not a solution of 10 - 5x = y.
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To describe the pattern in the table and extend it for x = 5, 6, and 7, we can observe that the value of y increases by 10 as x increases by 1.
The pattern can be described as follows:
For each increase of 1 in x, there is an increase of 10 in y.
Equation: y = 10x + 5
Extension for x = 5:
y = 10(5) + 5
y = 50 + 5
y = 55
Extension for x = 6:
y = 10(6) + 5
y = 60 + 5
y = 65
Extension for x = 7:
y = 10(7) + 5
y = 70 + 5
y = 75
Therefore, the extended pattern for x = 5, 6, and 7 is:
x: 5, 6, 7
y: 55, 65, 75