Solutions to Systems of Equations Flashcards

Questions and Answers

What is a system of equations?

An equation with only one variable

A single equation with multiple solutions

An equation that has no solution

A set of equations with the same variables (correct)

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?

Put each equation into slope-intercept form, graph, and find the intersection point. Signup and view all the answers

Match the following steps to solve a system of equations by substitution:

Isolate either variable from either equation = Step 1 Substitute into the other equation = Step 2 Solve = Step 3 Substitute answer into the other equation to find the other variable = Step 4 Signup and view all the answers

Match the following steps to solve a system of equations by combination:

Make sure all variables and signs line up = Step 1 Ensure cancelling variables have the same coefficient but different signs = Step 2 Add to combine = Step 3 Solve = Step 4 Substitute answer into one of the equations to find the other variables = Step 5 Signup and view all the answers

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.

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.