Algebra 1 - Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean for a system of equations to have no solution?

Back

A system has no solution when the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine if a system of equations has a unique solution?

Back

A system has a unique solution if the lines represented by the equations intersect at exactly one point.

Front

What is the substitution method in solving linear systems?

Back

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

Front

What is the elimination method in solving linear systems?

Back

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

Front

Solve the system: 24x - 6y = 12 and -24x + 6y = -12.

Back

Infinitely many solutions.

Front

Solve the system: 2x - 8 = 4y and 2y + 19 = 4x.

Back

(5, 1/2).

Front

Solve the system: 2x + 10y = -22 and 8x + 5y = 17.

Back

(4, -3).

Front

Solve the system: 4x - 11y = 5 and 20x - 55y = -30.

Back

No solution.