Solving Systems of Equations

Front

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

Back

The system has coinciding lines, meaning the equations represent the same line on a graph.

Front

What is the graphical representation of parallel lines in a system of equations?

Back

Parallel lines indicate that there is no solution to the system, as the lines never intersect.

Front

How do you find the solution to a system of equations graphically?

Back

The solution is the point where the two lines intersect on the graph.

Front

What is the solution to the system of equations: y = 2x - 11 and -3y = -6x - 15?

Back

No solution (the lines are parallel).

Front

What does the solution (1,3) represent in a system of equations?

Back

It represents the point where the two lines intersect, indicating the values of x and y that satisfy both equations.

Front

What are the steps to 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 are the steps to solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply if necessary to match coefficients. 3. Add or subtract the equations to eliminate one variable. 4. Solve for the remaining variable.

Front

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

Back

It means the lines are parallel and will never intersect.

Front

What is the solution to the system of equations: 4x - 2y = 7 and x + 2y = 3?

Back

x = 2, y = 1/2.

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.