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.