Algebra 1 Chapter 6 Study Guide Flashcards

Questions and Answers

What is the Graph and Check Method?

1: Graph both equations (slope intercept); 2: Estimate the coordinates of the point of intersection; 3: Check by substituting the points in the original linear system.

What is the solution when using the Graph and Check method for the equations x + 2y = 7 and 3x - 2y = 5?

(3,2)

What is the solution when using the Graph and Check method for the equations y = -x + 3 and y = x + 1?

(1,2)

What is the solution when using the Graph and Check method for the equations x - y = 2 and x + y = -8?

(-3,-5) Signup and view all the answers

What is the Substitution Method?

Step 1: Solve one of the equations for one variable; Step 2: Substitute the expression into the other equation and solve; Step 3: Substitute back to solve for the first variable. Signup and view all the answers

What is the solution when using the Substitution Method for the equations x = 17 - 4y and y = x - 2?

(5,3) Signup and view all the answers

What is the solution when using the Substitution Method for the equations 4x - 7y = 10 and y = x - 7?

(13,6) Signup and view all the answers

What is the solution when using the Substitution Method for the equations 2x = 12 and x - 5y = -29?

(6,7) Signup and view all the answers

What is the Addition/Subtraction method?

Step 1: Add or subtract the equations to eliminate 1 variable; Step 2: Solve the resulting equation for the other variable; Step 3: Substitute back into an original equation to find the eliminated variable. Signup and view all the answers

What is the solution when using addition for the equations x + 2y = 13 and -x + y = 5?

(1,6) Signup and view all the answers

What is the solution when using addition for the equations 3x - y = 30 and -3x + 7y = 6?

(12, 6) Signup and view all the answers

What is the solution when using subtraction for the equations 6x + y = -10 and 5x + y = -10?

(0,-10) Signup and view all the answers

What is the Multiplication method?

Step 1: Multiply to make coefficients opposites; Step 2: Add the equations; Step 3: Solve for y; Step 4: Substitute to solve for the other variable. Signup and view all the answers

What is the solution when using multiplication for the equations 4x + 5y = 35 and 2y = 3x - 9?

(5,3) Signup and view all the answers

What is the solution when using multiplication for the equations x + y = 2 and 2x + 7y = 9?

(1,1) Signup and view all the answers

What is the solution when using multiplication for the equations 4x - 3y = 8 and 5x - 2y = -11?

(-7, -12) Signup and view all the answers

Study Notes

Graph and Check Method

Involves graphing both equations in slope-intercept form.
Estimate intersection coordinates visually.
Verify by substituting the intersection point into the original equations.

Example Equations

For equations x + 2y = 7 and 3x - 2y = 5, intersection point is (3, 2).
For y = -x + 3 and y = x + 1, intersection point is (1, 2).
For x - y = 2 and x + y = -8, intersection point is (-3, -5).

Substitution Method

Step 1: Isolate one variable in one equation, ideally one with a coefficient of 1 or -1.
Step 2: Substitute this expression into the other equation.
Step 3: Solve for the second variable, then substitute back to find the first variable.

Example Problems Using Substitution

For equations x = 17 - 4y and y = x - 2, solution is (5, 3).
For 4x - 7y = 10 and y = x - 7, solution is (13, 6).
For 2x = 12 and x - 5y = -29, solution is (6, 7).

Addition/Subtraction Method

Step 1: Add or subtract equations to eliminate one variable.
Step 2: Solve the remaining equation for the other variable.
Step 3: Substitute back into one of the original equations to find the eliminated variable.

Example Problems Using Addition/Subtraction

For x + 2y = 13 and -x + y = 5, solution is (1, 6).
For 3x - y = 30 and -3x + 7y = 6, solution is (12, 6).
For 6x + y = -10 and 5x + y = -10, solution is (0, -10).

Multiplication Method

Step 1: Multiply equations as necessary to create opposite coefficients for one variable.
Step 2: Add equations to eliminate a variable.
Step 3: Solve for the remaining variable.
Step 4: Substitute back to find the value of the eliminated variable.

Example Problems Using Multiplication

For 4x + 5y = 35 and 2y = 3x - 9, solution is (5, 3).
For x + y = 2 and 2x + 7y = 9, solution is (1, 1).
For 4x - 3y = 8 and 5x - 2y = -11, solution is (-7, -12).

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Description

Prepare for your Algebra 1 exam with these comprehensive flashcards focused on Chapter 6. This study guide covers the Graph and Check Method, helping you understand how to graph equations and find intersection points. Perfect for reinforcing your knowledge and boosting your confidence!