Systems of Linear Equations All Methods

Front

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

Back

The graph consists of parallel lines.

Front

How many solutions does a system of equations have if it is inconsistent?

Back

0 solutions.

Front

Is (4, 1) a solution for the system of equations y = -x + 5 and y = 2x - 7?

Back

Yes, (4, 1) is a solution.

Front

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

Back

The solution is (4, 12).

Front

What is the solution to the system of equations 8x + 4y = 12 and y = -2x + 3?

Back

There are infinitely many solutions.

Front

What is a system of linear equations?

Back

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

Front

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

Back

It means the system has at least one solution.

Front

What is the graphical representation of a consistent system with exactly one solution?

Back

The graph shows two intersecting lines.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable.