Systems of 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

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

Solve the system of equations using substitution: \(y = 2x + 3\) and \(x + y = 9\).

Back

The solution is \((3, 9)\).

Front

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

Back

Skew lines are lines that do not intersect and are not parallel, existing in different planes.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

Solve by elimination: \(2x + 3y = 6\) and \(4x + 6y = 12\).

Back

The solution is infinite solutions, as the second equation is a multiple of the first.

Front

What happens when you graph the same equation twice?

Back

You will have infinite solutions.

Front

Solve by elimination: \(4x + 9y = 28\) and \(-4x - y = -28\).

Back

The solution is \((7, 0)\).

Front

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

Back

The graph consists of two intersecting lines.

Front

Solve by elimination: \(4x - 6y = -6\) and \(-2x - 12y = -12\).

Back

The solution is \((0, 1)\).