Systems of Equations (inc Word Problems)

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

Front

Define 'solution' in the context of a system of equations.

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

What is the difference between 'one solution', 'no solution', and 'infinitely many solutions'?

Back

One solution means the lines intersect at one point, no solution means the lines are parallel, and infinitely many solutions mean the lines coincide.

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and express them as a system.

Front

What is substitution in solving systems of equations?

Back

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

Front

What is elimination in solving systems of equations?

Back

Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

Write the system of equations for: 'The sum of two numbers is 10 and their difference is 2.'

Back

x + y = 10; x - y = 2.