If the operation # is defined by the equation x # y = 2x + y,what is the value of a in the equation 2 # a = a # 3 ?

a. 0
b. -1
c. 1
d. 1.5
e.-1.5
f. 2

just plug in the numbers:

2#a = 2*2+a
a#3 = 2a+3

so, now we have

4+a = 2a+3
a = 1

To find the value of a in the equation 2 # a = a # 3, we can substitute the given values into the operation # equation.

Using the equation x # y = 2x + y, we substitute 2 for x and a for y:

2 # a = 2(2) + a
2 # a = 4 + a

Now, we substitute a for x and 3 for y:

a # 3 = 2a + 3

Since we want to find the value of a that satisfies both equations, we can set them equal to each other:

4 + a = 2a + 3

Simplifying the equation:

a - 2a = 3 - 4
-a = -1
a = 1

Therefore, the value of a that satisfies the equation 2 # a = a # 3 is a = 1.

The correct answer is c. 1.

To find the value of a in the equation 2 # a = a # 3, we can substitute the operation with the given equation x # y = 2x + y.

Substituting 2 for x and a for y in the equation 2 # a = a # 3, we get:
2 # a = 2(2) + a
2 # a = 4 + a

Next, we substitute a for x and 3 for y in the equation a # 3:
a # 3 = 2a + 3

Since we want to find the value of a that satisfies the equation 2 # a = a # 3, we can equate the two expressions we found:
4 + a = 2a + 3

To solve for a, we will isolate the variables on one side:
a - 2a = 3 - 4
-a = -1

To get the value of a, we divide both sides of the equation by -1:
a = -1

Therefore, the value of a in the equation 2 # a = a # 3 is -1.