Solving Systems by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the solution of a system of equations?

Back

The point(s) (x, y) that satisfy all equations in the system.

Front

What does it mean if a system has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system has infinite solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine if a solution is correct?

Back

Substitute the values of the solution into both equations to see if they hold true.

Front

If x = 4, what is the value of y in the equation y = 2x + 1?

Back

y = 9.

Front

What is the first step in solving the system: y = 3x + 2 and 2x + y = 10?

Back

Substitute y from the first equation into the second equation.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions.

Front

What is the substitution method?

Back

A method for solving systems of equations by expressing one variable in terms of the other.