📄 8th Grade Math (Algebra I): Systems of Linear Equations Worksheet
📌 1. True / False
1. A system of linear equations consists of two or more linear equations with the same variables.
2. A system of linear equations can only have one solution.
3. The solution to a system of linear equations is the point where the graphs of the equations intersect.
4. The substitution method involves adding or subtracting equations to eliminate a variable.
5. If the graphs of two linear equations are parallel lines, the system has no solution.
✏️ 2. Fill in the Blanks
🔗 3. Matching
✍️ 4. Short Answer Questions
1. How can you verify if an ordered pair \((x, y)\) is a solution to a system of two linear equations?
2. Describe what it means for a system of linear equations to have 'no solution'.
🎯 5. Multiple Choice
1. Which of the following ordered pairs is a solution to the system of equations: \[ x + y = 7 \\ x - y = 3 \]
2. For which system of equations would the substitution method be most efficient?
3. If two lines in a system of linear equations are graphed and they are the same line, how many solutions does the system have?
📝 6. Open-Ended Questions
1. Solve the following system of equations by graphing:
\[
y = x + 1 \\
y = -2x + 7
\]
2. Solve the following system of equations using the substitution method:
\[
x + 2y = 10 \\
x = 4y - 2
\]
3. Solve the following system of equations using the elimination method:
\[
3x + 2y = 11 \\
-3x + 5y = 3
\]
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Name Surname: .................................. Date: .... / .... / 202...
Systems of Linear Equations Worksheet
|
SCORE
|
A. True (T) / False (F)
| ( .... ) | A system of linear equations consists of two or more linear equations with the same variables. |
| ( .... ) | A system of linear equations can only have one solution. |
| ( .... ) | The solution to a system of linear equations is the point where the graphs of the equations intersect. |
| ( .... ) | The substitution method involves adding or subtracting equations to eliminate a variable. |
| ( .... ) | If the graphs of two linear equations are parallel lines, the system has no solution. |
B. Fill in the Blanks
| 1) | A set of two or more linear equations with the same variables is called a .................... of linear equations. |
| 2) | When solving a system of equations by ...................., you graph each equation and find the point of intersection. |
| 3) | The .................... method involves solving one equation for a variable and then substituting that expression into the other equation. |
| 4) | If a system of linear equations has infinitely many solutions, the graphs of the equations are .................... lines. |
| 5) | The .................... method is useful when one variable in both equations has coefficients that are opposites or the same. |
C. Matching Concepts
| ( .... ) | Two or more linear equations considered together. | - Solution to a System |
| ( .... ) | An ordered pair \((x, y)\) that satisfies all equations in the system. | - Substitution Method |
| ( .... ) | Solving one equation for a variable and plugging that expression into the other equation. | - Elimination Method |
| ( .... ) | Adding or subtracting equations to remove one variable. | - System of Linear Equations |
| ( .... ) | Finding the point of intersection of the lines represented by the equations. | - Graphing Method |
D. Short Answer Questions
| 1) | How can you verify if an ordered pair \((x, y)\) is a solution to a system of two linear equations? |
| 2) | Describe what it means for a system of linear equations to have 'no solution'. |
E. Multiple Choice Questions
| 1) |
Which of the following ordered pairs is a solution to the system of equations:
\[
x + y = 7 \\
x - y = 3
\]
A) \((2, 5)\)
B) \((5, 2)\)
C) \((4, 3)\)
D) \((1, 6)\)
|
| 2) |
For which system of equations would the substitution method be most efficient?
A) \(2x + 3y = 10\)
\(2x - 3y = 2\)
B) \(y = 4x - 1\)
\(2x + y = 11\)
C) \(x + 2y = 5\)
\(3x - 2y = 7\)
D) \(5x + 6y = 20\)
\(3x + 2y = 12\)
|
| 3) |
If two lines in a system of linear equations are graphed and they are the same line, how many solutions does the system have?
A) Exactly one solution
B) No solution
C) Infinitely many solutions
D) Two solutions
|
F. Open-Ended Questions
| 1) |
Solve the following system of equations by graphing: \[ y = x + 1 \\ y = -2x + 7 \] |
| 2) |
Solve the following system of equations using the substitution method: \[ x + 2y = 10 \\ x = 4y - 2 \] |
| 3) |
Solve the following system of equations using the elimination method: \[ 3x + 2y = 11 \\ -3x + 5y = 3 \] |
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