Chapter 4 - Substitution and Elimination

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you solve the equation 5x + 3y = 7 for y?

Back

Rearranging gives y = (7 - 5x)/3.

Front

What does it mean to solve by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, allowing you to solve for the other variable.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

Front

Solve by substitution: y = 2/3x - 2 and y = -x + 3. What is the solution?

Back

(3, 0)

Front

Solve by substitution: 5x + 3y = 7 and y = 4. What is the solution?

Back

(-1, 4)

Front

Solve by elimination: -2x + y = 1 and 2x + y = 5. What is the solution?

Back

(1, 3)

Front

Solve by elimination: 2x − 3y = −1 and -x + y = −1. What is the solution?

Back

(4, 3)

Front

What is a system of equations?

Back

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

Front

What is the graphical interpretation of a solution to a system of equations?

Back

The solution is the point where the graphs of the equations intersect.