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

Front

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

Back

Isolate one variable in one of the equations.

Front

Given the equations y = 2x + 5 and -4x + y = 9, how do you solve for x?

Back

Substitute y from the first equation into the second: -4x + (2x + 5) = 9.

Front

What is the solution to the system of equations 5x + y = -10 and y = -6x - 13?

Back

(-3, 5) is the solution.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the graphical interpretation of a system of equations?

Back

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

Front

What does it mean if two equations have no solution?

Back

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

Front

What does it mean if two equations have infinitely many solutions?

Back

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

Front

What is the substitution method?

Back

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