Solving Systems using Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

Solving a system of equations using substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, meaning they have the same slope but different y-intercepts.

Front

What is the first step in solving the system y = 2x + 1 and y = 4x - 1 using substitution?

Back

The first step is to set the two equations equal to each other since they both equal y: 2x + 1 = 4x - 1.

Front

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

Back

The solution is (1, 3).

Front

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

Back

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

Front

How can you check if your solution to a system of equations is correct?

Back

You can check by substituting the solution back into both original equations to see if they hold true.

Front

What is the solution to the system y = 5x + 1 and y = 3x + 13?

Back

The solution is (6, 31).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines represented by the equations.

Front

What is the significance of the slope in a system of equations?

Back

The slope indicates the steepness of the line and helps determine if lines are parallel, intersecting, or coincident.