Solve, using the substitution method. d + e = 2 d – e = 4

Question

A) There are an infinite number of solutions.

B) There is no solution.

C) The solution is (3, –1).

D) The solution is (5, 1).

Answer 1

d + e = 2 ...............call that equation 1

d - e = 4 ................call that equation 2

 

in equation 1 lets solve for d

 

d + e = 2

+e crosses over the equality sign and becomes -e

so we have;

 

d = 2 - e ............call that equation 3

 

now substitute the value of d from eqn 3 into equation 2. 

We'd have

 

d - e = 4

 

(2 - e) - e = 4

 

2 - e - e = 4

 

2 - 2e = 4

collecting like terms we'll have

 

-2e = 4 - 2

-2e = 2

solving for e, divide both sides by -2

 

-2e/-2 = 2/-2

we'd have

 

e = -1

 

now that we know the actual value of e, we substitute it into eqn 1

 

d + e = 2

d + (-1) = 2

d - 1 = 2

and -1 crosses over the equality sign and become +1

so we have

 

d = 2 + 1

 

d = 3

 

 

so the solution for (d e) is (3 -1) respectively.

Answer 2

So your two equations are

d + e = 2

d − e = 4

 

In the substitution method, you solve one of these equations for a single variable, then substitute that into the other equation.

 

So let's solve d − e = 4 for d:

d − e = 4

(d − e) + e = (4) + e

d = 4 + e

 

Now, let's substitute this value for d in d + e = 2, then solve for e:

d + e = 2

(4 + e) + e = 2

4 + 2e = 2

(4 + 2e) − 4 = (2) − 4

2e = -2

(2e)/2 = (-2)/2

e = -1

 

Substituting this value for e in either equation:

d + e = 2

d + (-1) = 2

d − 1 = 2

(d − 1) + 1 = (2) + 1

d = 3

 

So we have the values d = 3, e = -1.  So your answer is C) The solution is (3, –1).

 

Now, you can always double-check your answer by plugging both values back into the two original equations:

d + e = 3 + -1 = 2

d - e = 3 − -1 = 4.

Answer 3

Hi Jamie;

You and I do not sleep.

d + e = 2

d – e = 4

Let's take the first equation and isolate one variable.  I randomly select d...

d + e = 2 

d=2-e

Let's plug this into the second equation...

d – e = 4

(2-e)-e=4

2-2e=4

-2e=2

e=-1

Let's plug this into either equation.  I randomly select the first...

d + e = 2

d+-1=2

d-1=2

d=3

Let's plug both results in the second equation...

d – e = 4

3--1=4

Subtracting a negative number is the same as adding a positive number.

3+1=4

4=4

Solution is (d,e) is (3,-1), C.