1. Solving Systems of Equations Using Substitution
Lesson 6-2

2. 4x – y = 75 (Since x = ______., ________ can be substituted
The solution of a system of equation scan be found using one of 3 methods:
________________________ , _________________________, or by _________________________ (The purpose of the substitution method is that once you find one of the values (either x or y), you can then substitute it into either of the original equations to find the other value.)
graphing
substitution
elimination
Ex. A x = 4y
4x – y = 75 (Since x = ______., ________ can be substituted
everywhere there is an “x” in the second equation.) 4y 4y
NOW use x = 4y to find the value of x. (Substitute the answer you just got for “4”)
x = 4y
___ ____________ Substitute
_______________ Simplify
4x – y = 75 Second equation
____________ Substitute “4y” for “x”
_____________ Simplify
_____________ Combine like terms
_____________ Divide both sides
4(4y) – y = 75
16y – y = 75
15y = 75
x = 4(5)
15y /15 = 75/15
x = 20
y= 5
The solution is ___________ (Don’t forget to write the solution, which is an ordered pair.)
(5, 20)

3. ________________ Second equation
Ex. B Solve y = 2x
3x + 4y = 11
  ________________ Second equation
________________ Substitute “2x” for “y”
_______________ Simplify
_______________ Combine like terms
_________________________ Divide both sides
____________________ Simplify
3x + 4y = 11
Use the first equation to find the value of x.
_______________ 1st equation
_______________ Substitute
_______________ Simplify
3x + 4(2x) = 11
3x + 8x = 11
y = 2x
11x = 11
y = 2(1)
11x/11= 11/11
y = 2
x = 1
The solution is ___________
(1, 2)

4. PRACTICE
1 x = 2y _____________________ ________________
4x + 2y = 15 ____________________ ________________
____________________ ________________
  ____________________ ____________________
_____________________
The solution is ___________

5. PRACTICE
2 y = 3x - 8 _____________________ ________________
y = 4 – x ____________________ ________________
____________________ ________________
  ____________________ ____________________
_____________________
The solution is ___________

6. PRACTICE:
3 2x + 7y = 3 _____________________ ________________
x = 1 – 4y ____________________ ________________
____________________ ________________
  ____________________ ____________________
_____________________
The solution is ___________

7. -2x – 3y = 14
4x + y = 12
4x + y = 12
-2x – 3(12 – 4x) = 14
4x – 4x + y = 12 – 4x
4(5) + y = 12
-2x – x = 14
y = 12 – 4x
20+ y = 12
10x – 36 = 14
20+ y – 20 = 12 – 20
10x – =
y = -8
10x = 50
10x/10 = 50/10
(5, -8)
x = 5

8. You can check your answer using the graphing calculator OR by substituting the ordered pair into each of the equations to see if it is a solution for each equation.

9. 2x + 2y = 8
2(2 – y) + 2y = 8
x + y = 2
4 – 2y + 2y = 8
x + y - y = 2 - y
4 = 8
x = 2 – y
4 = 8
false
no solutions
parallel lines

10. -6x +4y = -6
3x – 2y = 3
3x – 2y + 2y = 3 + 2y
-2(3+ 2y) +4y = -6
3x = 3 + 2y
(3x)/3 = (3 + 2y)/3
-6 – 4y +4y = -6
x = (3 + 2y)/3
-6 = -6
The statement ___________ is _________. There are ______ _______________________. The graphs of the lines are ________________________
-6 = -6
true
infinitely many
the same.

11. The school bookstore sells T-shirts for $8 and sweatshirts for $12
The school bookstore sells T-shirts for $8 and sweatshirts for $12. Last month, the store sold 37 T-shirts and sweatshirts for a total of $376. How many T-shirts were sold?
x = number of T-Shirts sold
Y = number of sweatshirts sold
x + y = 37
8x + 12y = 376
x + y = 37
y = 37 - x
8x + 12 y = 376
8x + 12 (37 – x) = 376
8x – 12x = 376
-4x = 376
-4x – 444 = 376 – 444
-4x = -68
x = 17
Equation based on the number of items sold
T-shirts were sold.
(so 20 sweatshirts were sold)
Equation based on the cost of items sold
Check:
17(8 ) + 12(20) = = 376

12. Watch the following videos for additional information on solving systems of equations using substitution.
Solving systems using substitution
Using Systems of Equations to Solve Real World Problems