WorksheetsMA.912.AR.9.6
Total questions: 25
Worksheet time: 2hrs 42mins
Solve the following systems of equations using substitution:
x = 6
y = 2x - 3
(6, 6)
(6, 9)
(9, 6)
(9, 9)
What is the solution of r - 11 = 5
11
14
15
16
What is the solution of 3w = 30
6
9
10
12
What is the first step when solving the system?
Isolate x
Solve for y
Sub in the expression in terms of y
Sub in the expression in terms of x
What is the first step when solving the following?
Eliminate the x's
Plug in the expression in terms of y
Eliminate the y's
Plug in the expression in terms of x
What is the first step to solve the following?
Eliminate the x's
Eliminate the y's
Multiply both equations by the LCM of x
Multiply one equation by -1
When solving a system of equations algebraically, which statement results in no solution?
4 = 7
-2 = 2
-3 = 3
all of the above
When solving a system of equations algebraically, which statement results in infinite solutions?
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 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
4x + 8y = 20
-4x + 2y = -30
You and your friend are participating in the hot air balloon festival! Your balloon is currently 200 feet in the air, and descending at a rate of 3ft per sec. Your friend is 75 feet in the air, an ascending at a rate of 2ft per sec. After how many seconds will you both be at the same height? Write the equation.
200+3x=75-2x
200-3x=75+2x
200-3x=75-2x
200+3x=75+2x
Solve for y: 3y +1 = 2y +6
(a)
y = 8.40 + x
y = 8.40x + 58
y = 8.40x
y = 8.40x - 58
y = 8
Pilar had brochures printed for a new business venture. Pilar originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Pilar spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?
x+y=134
x+y=120
3x+3y=134
4x+3y=120
4x+3y=134
3x+3y=120
7xy=134
6xy=120
Saulo is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, Saulo made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
1.5x+0.5y=78.5
x+y=87
1.5x+0.5y=78.5
1.5x+0.5y=87
x+y=78.5
1.5x+0.5y=87
x+y=78.5
x+y=87
Scott's Automotive charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie was charged $63.
35x + 7 = 63
7x = 63
7x - 35 = 63
7x + 35 = 63
