SoE- Substitution & Elimination

Front

What is the substitution method in solving systems of equations?

Back

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

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: 9x - 4y = 7 and x - 4y = -17.

Back

(3, 5)

Front

Solve for x and y using substitution: 3x + 2y = 16 and y = -7x + 19.

Back

(2, 5)

Front

Solve for x and y using substitution: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)

Front

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

Back

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

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

Solve the system using substitution: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)

Front

Solve by elimination: -8x - 10y = 20 and -8x - 6y = -4.

Back

(5, -6)

Front

What is a system of equations?

Back

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