4.2 Systems - Graphing/Elimination/Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

Solve by substitution: 5x + 3y = 7, y = 4

Back

(-1, 4)

Front

Solve by substitution: y = 2/3x - 2, y = -x + 3

Back

(3, 0)

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 remaining variable.

Front

Solve by elimination: 2x − 3y = −1, -x + y = −1

Back

(4, 3)

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

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

Back

It means that the equations represent the same line, and thus every point on the line is a solution.

Front

Solve: 2x + 3y = 6, x - y = 1

Back

(3, 0)

Front

Solve: 4x - 2y = 8, 2x + y = 4

Back

(4, -2)