Question

The pairs of equations below are equivalent. Determine what was done to the first equation in order to obtain the second equation. (For example, everything multiplied by 5 or Multiplicative Property of Equality) If more than one operation was performed please indicate the operations and the order they were performed?

1). x + y = 5 3x+3y=15
2). 4x+3y=12 x+3/4y=3
3). 6x+4y=20 y= -3/2x +5​

Answer 1

The operations performed to transform each pair of equations include multiplication by 3, division by 4, and subtraction after division by 4 to isolate the variable on one side.

Step-by-step explanation:

The pairs of equations given are equivalent. To understand what operations were performed to go from the first equation to the second one in each pair, let's examine them one by one.

x + y = 5 to 3x+3y=15: Here, both sides of the first equation were multiplied by 3. This is known as the Multiplicative Property of Equality. Multiplying each term on the left side by 3 gives us 3x + 3y, and multiplying 5 by 3 on the right side gives us 15, resulting in the second equation.

4x+3y=12 to x+3/4y=3: The first equation is divided by 4 on both sides. Dividing the term 4x by 4 yields x, and dividing 3y by 4 yields 3/4y. Similarly, dividing 12 by 4 gives 3. The resulting equation is x+3/4y=3.

6x+4y=20 to y= -3/2x +5: To obtain the second equation, the first equation is divided by 4 and then rearranged. Dividing by 4 gives 3/2x + y = 5. Then, by subtracting 3/2x from both sides, we get y = -3/2x + 5.