Systems of Equations (Substitution)

Show your work for each problem.

1.
In the system , which equation should you substitute INTO?
1. a)
2. b)Neither equation
3. c)Either one works the same
4. d)
Answer:
Since already has isolated, we substitute this expression into the OTHER equation to solve for .
2.
Solve for :
Answer: 3
Substitute into : , so , therefore .
3.
What is the first step to solve by substitution?
1. a)Multiply both equations by 3
2. b)Isolate or in one equation
3. c)Graph both equations
4. d)Add the equations together
Answer: Isolate or in one equation
The substitution method starts by isolating one variable. From , we can get , then substitute into the other equation.
4.
Solve for :
Answer: 3
Substitute into : , so , therefore .
5.
Solve the system:
Answer: (3, 2)
1. Substitute into the second equation. What do you get? 2x + (x - 1) = 8
2. Simplify: . Solve for . 3
3. Now find using . 2
6.
Solve the system:
1. a)
2. b)
3. c)
4. d)
Answer:
Substitute: . Then . Solution: .
7.
Solve for :
Answer: 4
From equation 1: . Substitute into equation 2: .
8.
Solve:
Answer: (3, 5)
1. Substitute into . What equation do you get? 2(y - 2) + y = 11
2. Distribute and simplify: . Solve for . 5
3. Find using . 3
9.
Solve:
Answer: (20/7, 11/7)
1. Isolate from the second equation: x = 6 - 2y
2. Substitute into the first equation: . Simplify. 18 - 6y - y = 7
3. Solve for : 11/7
10.
What happens when you solve by substitution?
1. a)No solution ()
2. b)One solution
3. c)One solution
4. d)Infinitely many solutions ()
Answer: Infinitely many solutions ()
Substitute: (always true). This means infinitely many solutions - the equations represent the same line.
11.
Solve for :
Answer: 25/7
Substitute : .
12.
A movie theater sold 200 tickets. Adult tickets cost 15 euros and child tickets cost 10 euros. Total revenue was 2500 euros. How many adult tickets were sold?
Answer: 100
1. Let = adult tickets, = child tickets. Write the total tickets equation. a + c = 200
2. Write the revenue equation. 15a + 10c = 2500
3. Isolate from the first equation. c = 200 - a
4. Substitute and solve for . 100
13.
Solve:
Answer: (-6, -17)
1. Substitute into . What do you get? 5x - 2(3x + 1) = 4
2. Distribute: . Simplify and solve for . -6
3. Find using . -17
14.
What happens when you solve by substitution?
1. a)One solution
2. b)No solution ()
3. c)Infinitely many solutions
4. d)One solution
Answer: No solution ()
Substitute: (false). This means no solution - the lines are parallel.
15.
A chemist needs 500 mL of a 40% acid solution. She has a 25% solution and a 50% solution. How many mL of the 50% solution should she use?
Answer: 300
1. Let = mL of 25% solution, = mL of 50% solution. Write the volume equation. x + y = 500
2. Write the acid concentration equation (40% of 500 = 200 mL pure acid). 0.25x + 0.50y = 200
3. From the first equation, isolate . x = 500 - y
4. Substitute and solve for (50% solution). 300