solving systems of equations by substitution

Front

What is a system of equations?

Back

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

Front

What does substitution mean in solving equations?

Back

Substitution is the process of replacing one variable with an expression that contains another variable.

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the other variable.

Front

What is the solution to a system of equations?

Back

The solution is the point where the equations intersect, representing the values of the variables that satisfy all equations in the system.

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, and every point on that line is a solution.

Front

Given the equations y = 2x + 1 and y = 4x - 1, how do you find the solution?

Back

Set 2x + 1 equal to 4x - 1, solve for x, then substitute back to find y.

Front

What is the first step in solving the system x + 2y = 2 and x = -4y + 2 by substitution?

Back

Substitute -4y + 2 for x in the first equation.

Front

If y = -7x - 15, what is y when x = -2?

Back

y = -7(-2) - 15 = 14 - 15 = -1.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection of the lines on a coordinate plane.