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Subtraction property of equality is used when u have 2 sides with an equal sign in the middle and u want to subtract from both sides.
Example :
2x + 3 = 7 ....subtract 3 from both sides
2x + 3 - 3 = 7 - 3
2x = 4
x = 4/2
x = 2
When subtracting real numbers..if the numbers are on the same side of the equal sign...u can just subtract on that one side
Example :
2x = 7 - 3
2x = 4
x = 4/2
x = 2
Answer:
- b. y = 2/3x +5
- c. y = -3 or -1/2
Step-by-step explanation:
b. The particualar steps for solving a linear equation such as this may vary from one equation to another. In general, you want to put all the y-terms on one side of the equal sign and everything else on the other side. Here's how we'll do that in this case.
Use the distributive property to eliminate parentheses.
... 6x -3y +12 = 4x -3
Find the unwanted terms on the side of the equation where y is, then add their opposite. In this case, we're adding -(6x+12)
... -3y = (4x -3) -(6x +12) = -2x -15
Divide by the coefficient of y.
... y = -2x/(-3) -15/(-3)
... y = 2/3x +5
____
c. This is a 2nd-degree (quadratic) equation with y as its only variable. The factor (2y+1) appears in both terms so we can use the distributive property to factor it out. Then the equation becomes ...
... (y +3)(2y +1) = 0
The zero product rule tells us this product will be zero only when one or the other of the factors is zero. This fact helps us find the values of y that are the solution to the equation.
For y+3 = 0:
... y + 3 = 0
... y = -3 . . . . . . add -3 to both sides of the equation
For 2y +1 = 0:
... 2y +1 = 0
... y +1/2 = 0 . . . . divide by 2
... y = -1/2 . . . . . . add -1/2
The solutions are y = -3 or y = -1/2.
D. The number of items (items being numbers)
We know that
X²+y²=9 -------> X²+y²=3²
is the equation of a circle with center (0,0) and radius r=3 units
so
<span>the translation of four units to the right and three units down is equals to move the center (0,0)--------> (0+4,0-3)------> (4.-3)
the new center of the circle is (4,-3)
the new equation is
(x-4)</span>²+(y+3)²=3²
see the attached figure
