## 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?

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What is the Substitution Method?

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

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

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

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What is the Addition/Subtraction method?

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

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

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

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What is the Multiplication method?

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

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

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

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## 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!