Writing Systems of Equations

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

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships into equations, and ensure the equations reflect the problem's constraints.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines (or curves) on a coordinate plane, where the intersection points represent the solutions.

Front

What is the elimination method for 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.

Front

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

Back

Identify the unknowns, create equations based on the relationships described, and ensure they reflect the total quantities involved.

Front

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

Back

Front

How do you find the y-intercept of a linear equation?

Back