Systems of equations: Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do 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

The equations represent the same line, meaning every point on the line is a solution.

Front

What is the y-intercept of a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, y).

Front

How can you find the y-intercept from an equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the slope of a line?

Back

The rate of change of y with respect to x, often represented as 'm' in the equation y = mx + b.

Front

How do you find the slope from two points?

Back

Use the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be parallel?

Back

They have the same slope but different y-intercepts.