Solving Systems by 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 by substitution?

Back

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

Front

Given the equations y = 2x + 1 and y = 4x - 1, how do you find the value of x?

Back

Set the equations equal to each other: 2x + 1 = 4x - 1.

Front

What is the first step in solving the system y = 3x - 8 and y = 4 - x by substitution?

Back

Solve one of the equations for y or x.

Front

If y = -2x + 18 and y = 8, how do you find x?

Back

Set -2x + 18 = 8 and solve for x.

Front

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

Back

(1, 3)

Front

How do you check if (3, 1) is a solution to the system y = 3x - 8 and y = 4 - x?

Back

Substitute x = 3 and y = 1 into both equations to see if they hold true.

Front

What does it mean if two lines intersect at a point in a system of equations?

Back

It means there is one unique solution to the system.

Front

What is the graphical representation of a system of equations?

Back

The equations are represented as lines on a graph, and their intersection point represents the solution.

Front

What is the significance of the slopes of the lines in a system of equations?

Back

The slopes determine whether the lines are parallel, intersecting, or coincident.