LP 3 Assessment Algebra 1

Front

What is a system of linear equations with no solution?

Back

A system of linear equations has no solution when the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Front

Solve the system: x = -3y - 17 and 2x + 3y = -7.

Back

(10, -9)

Front

When can equations be combined using elimination?

Back

Equations can be combined using elimination to eliminate a variable ONLY if there are exact opposite terms (opposite signs).

Front

Solve the system: 3x + 2y = 8 and -x + y = -11.

Back

(6, -5)

Front

What is the result of adding the equations -8x + 9y = -25 and 5x - 9y = 19?

Back

-3x = -6

Front

Define a linear equation.

Back

A linear equation is an equation that represents a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

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 variable.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if a system of equations is consistent or inconsistent?

Back

A system of equations is consistent if it has at least one solution (the lines intersect), and inconsistent if it has no solutions (the lines are parallel).