Algebra 1 Chapter 6 Study Guide Flashcards

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).