Topic 4 Systems of Equations Review

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to intersect?

Back

When two lines intersect, it means they cross at a point, which represents the solution to the system of equations.

Front

What is the solution to a system of equations?

Back

The solution is the set of values for the variables that make all equations in the system true.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the Slope-Intercept Form of a linear equation?

Back

The Slope-Intercept Form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph a linear equation in Slope-Intercept Form?

Back

To graph, start at the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

Front

What is the Standard Form of a linear equation?

Back

The Standard Form is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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

Back

No solution means the lines are parallel and will never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same line, meaning they intersect at every point on that line.

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations and manipulate them to eliminate one variable.