Solving System of Equations by Graphing & Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved simultaneously.

Front

What does it mean to solve a system of equations by graphing?

Back

It involves plotting the equations on a graph and identifying the point(s) where the lines intersect, which represents the solution.

Front

What is substitution in the context of solving equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

What is the solution to a system of equations?

Back

The values of the variables that satisfy all equations in the system.

Front

What does it mean if two lines on a graph are parallel?

Back

It means the system of equations has no solution, as the lines never intersect.

Front

What does it mean if two lines on a graph coincide?

Back

It means the system of equations has infinitely many solutions, as the lines overlap completely.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are satisfied, it is a solution.

Front

What is the first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

Solve the system by substitution: y = 2x + 3, 4x - y = 1.

Back

(1, 5) is the solution.

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Solve the system by graphing: x + y = 5, x - y = 1.

Back

(3, 2) is the solution.