Solving Systems Using Graphing and 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 graphically?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is substitution in the context of solving equations?

Back

Substitution is a method where you solve one equation for a variable and then substitute that expression into another equation.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

Front

What is the graphical representation of the equation y = 11?

Back

A horizontal line at y = 11 on the graph.

Front

What is the solution to the system of equations y = 3x + 9 and y = -6?

Back

(-5, -6) is the solution.

Front

How do you solve the system of equations y = 8 and y = -4x + 4 using substitution?

Back

Substitute y = 8 into the second equation to find x, resulting in (-1, 8).

Front

What does the solution (6, 11) represent in the context of a system of equations?

Back

It represents the point where the two equations intersect on a graph.

Front

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

Back

Solve one of the equations for one variable in terms of the other.

Front

What is the solution to the system of equations y + 4x = 35 and y = 11?

Back

(6, 11) is the solution.