Questions and Answers
What is a system of equations?
What is the solution of a system of equations?
An ordered pair that satisfies all equations in the system.
What does it mean to solve by graphing?
To find where lines intersect.
How do you graph an equation?
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Match the following steps to solve a system of equations by substitution:
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Match the following steps to solve a system of equations by combination:
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Study Notes
System of Equations
- Defined as a set of equations sharing the same variables.
- Solutions are ordered pairs satisfying all included equations, e.g., ( x + 2y = 5 ) and ( 2x - 3y = 3 ).
Solution of a System of Equations
- The solution must satisfy all equations within the system.
- Typically represented as an ordered pair.
Solve by Graphing
- Involves determining the point of intersection for the graphed lines of the equations.
How to Graph
- Convert each equation into slope-intercept form.
- Graph the equations on the same coordinate plane.
- Identify the solution at the point where the lines intersect.
Substitution Method
- Isolate one variable in either equation.
- Substitute the isolated variable into the other equation.
- Solve for the substituted variable.
- Use the obtained solution to find the remaining variable by substituting back.
Combination Method (Elimination)
- Ensure all variables and signs are aligned properly.
- Identify variables meant for cancellation that have equal coefficients with opposite signs.
- Add equations to combine and eliminate a variable.
- Solve for one variable and substitute it back into one of the original equations to find the other variable.
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Description
Explore essential terms and definitions related to systems of equations with these flashcards. Learn to identify and solve systems of equations by different methods, including graphical solutions. Perfect for students studying algebra concepts.