Solving Systems of Equations - Algebra 1

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect and have no solutions.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How many solutions does a system of equations with two intersecting lines have?

Back

One solution.

Front

What is the solution to the system of equations: 5x + 3y = 7 and y = 4?

Back

(-1, 4).

Front

What is the solution to the inequality 4x - 3y ≥ 18 for the point (0, -6)?

Back

True, (0, -6) satisfies the inequality.

Front

What is the output variable in the equation 7y + 4x = 10?

Back

y.

Front

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

Back

It means the lines are parallel and do not intersect.