Solve Systems by 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 by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

Isolate one variable in one of the equations.

Front

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

Back

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

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

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the solution to the system: y = 2x + 3 and y = -x + 1?

Back

(2, 7) - found by substituting x=2 into either equation.

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines representing the equations.

Front

What is the significance of the slope in a linear equation?

Back

It indicates the steepness and direction of the line; positive slope means the line rises, negative means it falls.

Front

What is the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.