Question

Solve the system of linear equations with substitution;

Answer 1

Let's solve for x.
x
+
4
y
=
(
14
)
(
3
)
x
+
7
y
Step 1: Add -42x to both sides.
x
+
4
y
+
−
42
x
=
42
x
+
7
y
+
−
42
x
−
41
x
+
4
y
=
7
y
Step 2: Add -4y to both sides.
−
41
x
+
4
y
+
−
4
y
=
7
y
+
−
4
y
−
41
x
=
3
y
Step 3: Divide both sides by -41.
−
41
x
−
41
=
3
y
−
41
x
=
−
3
41
y
Answer:
x
=
−
3
41
y

Answer 2

Solve the system of linear equations with substitution;

x+4y=14   Equation 1
3x+7y=22 Equation 2

Solve Equation 1 for x 

x + 4y = 14     Isolate the variable by moving the second variable to the other side using the inverse operation which in this case is subtraction. So.....
x + 4y =  14
   -  4y = -4y
x        = 14 - 4y

Now insert your answer above into Equation 2.

3x + 7y = 22
3(14 -4y) + 7y = 22           Now distribute to eliminate parenthesis
42 - 12y + 7y = 22            

 42 - 5y = 22                      Combine like terms and remember the 12 is  
-42         -42                       technically negative
      -5y  =  -20                   Isolate the variable which in this case we divide
   -5y/-5 =  -20/-5
       y =  4

Going back to Equation 1. Insert the know variable to solve for x.

x+4y=14   Equation 1

x + 4(4) = 14
x + 16 = 14          Isolate the variable by subtracting 16 from both sides
  - 16    -16
x = -2

The solution is an ordered pair (x,y) ........ (-2, 4).

Check your work by inserting the ordered pair into either of the equations.

x+4y=14   Equation 1

-2 + 4(4) = 14
-2 + 16 = 14
        14 = 14

3x+7y=22 Equation 2

3(-2) + 7(4) = 22
-6 + 28 = 22
       22 = 22