Systems of Linear Equations Review

Front

What is a system of linear equations?

Back

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

Front

What does it mean if a system of linear equations has one solution?

Back

It means that the graphs of the equations intersect at exactly one point, indicating a unique solution.

Front

What does the graph of a system of linear equations with no solution look like?

Back

The graph consists of parallel lines that never intersect.

Front

What does the graph of a system of linear equations with infinite solutions look like?

Back

The graph consists of the same line represented by multiple equations, meaning every point on the line is a solution.

Front

How do you solve a system of linear equations using substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of linear equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of the solution (1, -1) in a system of equations?

Back

The point (1, -1) is the intersection point of the two lines represented by the equations in the system.

Front

What is the significance of the coefficients in a system of linear equations?

Back

The coefficients determine the slope and position of the lines in the graph, affecting the number of solutions.

Front

What is the first step in solving the system of equations x + 2y = -3 and x - y = -12?

Back

You can use either substitution or elimination; for substitution, solve one equation for x or y first.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, which can be either one solution or infinitely many solutions.