Algebra 1 EOC Review(#21-40)

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the graphs of the equations intersect.

Front

What does it mean for a system of linear equations to have multiple common coordinate pairs?

Back

It means that the equations represent the same line, resulting in an infinite number of solutions where every point on the line is a solution.

Front

How do you determine the number of solutions in a system of linear equations?

Back

1. If the lines intersect at one point, there is one solution. 2. If the lines are parallel, there are no solutions. 3. If the lines are the same, there are infinitely many solutions.

Front

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

Back

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

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the meaning of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.

Front

What is the difference between a one-to-one function and a many-to-one function?

Back

A one-to-one function has a unique output for every input, while a many-to-one function can have the same output for different inputs.

Front

How do you interpret the solution of a word problem involving a system of equations?

Back

Identify the variables, set up the equations based on the problem's context, and solve the system to find the values of the variables.