WorksheetsSolving System of Equations by Substitution Method
Total questions: 18
Worksheet time: 53mins
When solving a system of equations algebraically, which statement results in infinite solutions?
4 = 7
2 = 2
-3 = 3
all of the above
When solving a system of equations algebraically, which statement results in no solution?
4 = 7
-2 = 2
-3 = 3
all of the above
Example 1
Steps 1 and 2a:
Step 1: Solving for a variable.
Step 2a: Substitute
y = 6x
2x + 5y = 32
This step is what EOC likes to test on!
The variable is already isolated, so we've already solved the system.
The variable is already isolated for y, so we substitute it in the second equation like this:
2(6x) + 5y = 32
The variable is already isolated for y, so we substitute it in the second equation like this:
2x + 5(6x) = 32
Example 1
Step 2 part b: Solve answer from step 2 part a.
Solve 2x + 5(6x) = 32
x = 0
x = 1
x = -1
x = 4
Example 1
Step 3:
After substituting the first equation into the second one and working it out, I got
x = 1.
What should I do next? Then do it.
Fill in 1 for x in y = 6x
y = 6(1)
y = 6
Fill in 1 for y in y = 6x
1 = 6x
1/6 = x
Fill in 1 for y in 2x + 5y = 32
2x + 5(1) = 32
2x + 5 = 32
2x = 27
x = 27/2
Example 1
Step 4:
What is the solution to the system:
y = 6x
2x + 5y = 32
Given I got x = 1 from step 2 and y = 6 from step 3.
(1, 6)
(6, 1)
Example 2:
x - y = 0
18x + 2y = 0
Which statement would be correct for step 1 and do it?
I would solve the first equations for y because it has a coefficient of 1.
y = -x
I would solve the first equations for y because it has a coefficient of -1.
-y = -x
I would solve the first equations for x because it has a coefficient of 1.
x = y
Example 2:
x - y = 0
18x + 2y = 0
Step 2:
In step 1, we got x = y.
Which shows the correct steps for step 2 (substituting and solving)?
18x + 2y = 0
18(y) + 2y = 0
20y = 0
No Solution
18x + 2y = 0
18(y) + 2y = 0
20y = 0
y = 0
Example 2:
x - y = 0
18x + 2y = 0
Step 3:
In step 2, we got y = 0.
What do I next? Do it.
I will plug y = 0 into the equation x = y.
x = y
x = (0)
x = 0
I will plug y = 0 into the equation x = y.
x = y
(0) = y
0 = y
Example 2:
x - y = 0
18x + 2y = 0
Step 4:
In step 2, we got x = 0 and y = 0, what is the final answer?
(a)
Example 3:
y = 4 - 2x
-4x - 2y = -8
Which statement is correct to begin to solve this equation?
The variable is already isolated in the first equation, so we have already solved it.
The variable is already isolated in the first equation, so we have to plug into the second one like this:
-4(4-2x) - 2y = -8
The variable is already isolated in the first equation, so we have to plug into the second one like this:
-4x - 2(4 - 2x) = -8
Example 3:
y = 4 - 2x
-4x - 2y = -8
Finish step 2 (which shows correct steps):
-4x - 2(4 - 2x) = -8
-4x - 2(4 - 2x) = -8
-4x - 8 + 4x = -8
8 = -8
-4x - 2(4 - 2x) = -8
-4x - 8 - 4x = -8
-8x - 8 = -8
-8x = 0
x = 0
-4x - 2(4 - 2x) = -8
-4x - 8 + 4x = -8
-8 = -8
-4x - 2(4 - 2x) = -8
-4x - 8 - 2x = -8
-6x - 8 = -8
-6x = 0
x = 0
Example 3:
y = 4 - 2x
-4x - 2y = -8
In step 2, we got -8 = -8.
What does this mean?
The answer is
(-8, -8).
Infinitely Many Solutions
No Solution
We made a mistake.
Solve for the system of equations using substitution.
4x + y = 8
x=5 − y
(4, 1)
(1, 4)
(-2, 0)
No solution.
Solve for the system of equations using substitution.
(-6, 1)
(-12, -12)
(1, -6)
No solution
Infinite solutions
Solve for the system of equations using substitution.
No Solution
(2, 2)
(-1, 2)
(-1, -2)
Solve the system of equations by substitution.
-x + y = -13
-8x - 4y = -8
