Systems of Equations Substitution

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 to solve a system of equations using substitution?

Back

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

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect on a graph.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an equivalent expression from another equation.

Front

Given the equations y = 2x + 3 and y = -x + 1, how do you solve using substitution?

Back

Set 2x + 3 = -x + 1 and solve for x, then substitute back to find y.

Front

What is the first step in solving the system 2y + x = -15 and x = 3y using substitution?

Back

Substitute 3y for x in the first equation.

Front

If you have the equations 5x - 4y = -3 and y = -3x + 5, how do you solve them?

Back

Substitute -3x + 5 for y in the first equation and solve for x.