The value of c that makes the equations c+d=6 and c-2d=3 true is:
A) 1
B) 2
C) 3
D) 4
E) 5
The answer is 5, but I don't know why. Please explain?
c+d=6 and c-2d=3
c = 6 - d
Substitute that value in the second equation.
6 - d - 2d = 3
-3d = - 3
d = 1
~~~~~~~~~~~~~~~~~~~~~~~~~
c + d = 6
c + 1 = 6
c = 5
Thank you! I'm studying for the College Board, so this really helped!
You're very welcome. Good luck with your exam! :-)
To find the value of c that makes the equations c+d=6 and c-2d=3 true, we can use the method of substitution or elimination.
Let's start with the substitution method.
First, let's solve the first equation c+d=6 for c. We can isolate c by subtracting d from both sides of the equation:
c = 6 - d
Now, substitute this value of c into the second equation c-2d=3:
(6 - d) - 2d = 3
Simplify the equation by combining like terms:
6 - 3d = 3
To isolate the variable, subtract 6 from both sides:
-3d = -3
Divide both sides of the equation by -3 to solve for d:
d = 1
Now that we have found the value of d, we can substitute it back into the first equation to find the value of c:
c + 1 = 6
Subtract 1 from both sides:
c = 5
Therefore, the value of c that makes both equations true is c = 5.
The correct answer is E) 5.