Systems of Equations (Graphing and Substitution) Flashcard review

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the graphing method in solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the point of intersection is the solution.

Front

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

Back

Substitute the point's coordinates into both equations; if both equations are true, the point is a solution.

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

(1, 5) - The point where the two lines intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How can you find the point of intersection of two lines graphically?

Back

By plotting both lines on a graph and identifying the coordinates where they cross.

Front

What is the first step in using the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.