Solving Systems by Substitution

Front

What is the substitution method in solving systems of equations?

Back

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

Front

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

Back

Make sure at least one equation is solved for one variable.

Front

What does it mean if a system of equations has no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What is the standard form of a linear equation?

Back

The standard form is expressed as Ax + By = C, where A, B, and C are integers.

Front

How do you identify parallel lines in a system of equations?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is expressed as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the purpose of substitution in solving systems of equations?

Back

Substitution allows us to reduce the number of variables in the equations, making it easier to find the solution.

Front

If you have the equations y = 2x + 3 and 4x - y = 1, how would you use substitution?

Back

Substitute y from the first equation into the second equation: 4x - (2x + 3) = 1.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the lines are parallel.