4.1-4.3 Solving Systems of Equations

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 for two equations to intersect on a graph?

Back

It means that the equations have a common solution, represented by the point where their graphs meet.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

Back

(3, 1)

Front

What is the solution to the system of equations x = -3y - 17 and 2x + 3y = -7?

Back

(10, -9)

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.