GCW - Solving Systems by Graphing & Substitution Methods

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations in the same variable.

Front

What does it mean if a system has no solution?

Back

It means that the lines represented by the equations do not intersect; they are parallel.

Front

What does it mean if a system has infinitely many solutions?

Back

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

Front

How do you determine the solution of a system of equations graphically?

Back

The solution is the point where the graphs of the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

It is a straight line with a slope of 2 and a y-intercept of 1.

Front

How can you tell if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

The solution is the point of intersection, which can be found by solving the equations simultaneously.

Front

What does it mean for a system to have one solution?

Back

It means that the lines intersect at exactly one point.

Front

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

Back

Isolate one variable in one of the equations.