Questions and Answers
What is the value of x when solving the equation 5x + 1 = -9?
What is the solution in a system of equations?
The point where the lines intersect.
What is the first step in solving a system of equations using substitution?
Solve one equation for a variable.
After substituting an expression for a variable, what is the next step?
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What do you do in Step 3 of solving systems by substitution?
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What is the final step after solving the system of equations?
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In the equation y = 2x + 1, if x = -2, then y equals -3.
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What happens when you multiply a variable by y?
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Given the example x + 2y = 6, what is x when y = -1?
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Study Notes
Solving Systems by Substitution
- The equation set y = 2x + 1 and 3x + y = -9 can be combined to form a single equation by substitution.
- Combining and simplifying yields 5x + 1 = -9.
- To isolate x, subtract 1 from both sides, leading to 5x = -10.
- Dividing both sides by 5 results in x = -2.
- To find y, substitute x into the equation y = 2x + 1, leading to y = 2(-2) + 1 = -4 + 1 = -3.
- The solution where the two lines intersect is represented by the ordered pair (-2, -3).
Steps to Solve by Substitution
- Step 1: Solve one equation for a variable, preferably with a coefficient of 1 or the simplest form.
- Step 2: Substitute the derived expression into the other equation to solve for the remaining variable.
- Step 3: Substitute the result back into one of the original equations to find the value of the other variable.
- Step 4: Represent the final solution as an ordered pair.
Important Note
- When multiplying out terms that involve a variable, ensure to distribute the multiplication across all terms inside the parentheses accurately.
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Description
This quiz provides flashcards to help you understand the method of solving systems of equations by substitution. Each card illustrates key concepts and processes involved in finding solutions. Use these flashcards to enhance your skills and prepare for your Algebra 1 examinations.
