WARM UP Solve the linear system using substitution.

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SYSTEMS OF LINEAR EQUATIONS

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WARM UP Solve the linear system using substitution. 1. 2x + y = 12; 3x – 2y =11 2. One auto repair shop charges $30 for a diagnosis and $25 per hour for labor. Another auto repair shop charges $35 per hour for labor. For how many hours are the total charges for both shops the same?

Career Day Friday January 23 For all 8th graders Lasts the entire school day Wear proper attire (clothes) No t-shirts or jeans 7th graders will have an assignment and report to another room – to be determined

Solving Linear Systems using Elimination The use of elimination means you are adding or subtracting the equations to eliminate one of the variables. This can only be done when the coefficients of one of the variables are the same or opposites. Both equations must be in the same form, with elimination have both equations in standard form (Ax + By = C)

Solving Linear Systems using Elimination Example: 3x + 4y = 8 -3x + 5y = 10 What do you notice about the coefficients of the x-variable? Would you add or subtract these 2 equations to eliminate the x-variable?

Solving Linear Systems using Elimination If the coefficients are opposites, then add the 2 equations. If the coefficients are the same, then subtract the 2 equations.

Solving Linear Systems using Elimination Working through the example: Now substitute 2 for y in either one of the equations to find the value of x.

Solving Linear Systems using Elimination Example 2: 5x + 6y = 4; 7x + 6y = 8 Substitute 2 for x in either one of the equations to find the value of y.

Using your graphing calculator You can use a graphing calculator to check the solution of a linear system. 1. Put both equations in slope-intercept form. 2. Enter these equations into the calculator. 3. Push graph 4. Hit the 2nd key then trace, the ‘Calculate’ screen will appear. 5. Go down to #5 – intersect. Press enter until the word ‘intersection’ appears on the screen. 6. The calculator will show the coordinates of the intersection point of the 2 lines.

Guided Practice Solve these linear systems using elimination. Check your solutions by using your graphing calculator. 1. 4x – 3y = 5; -2x + 3y = -7 2. 7x – 2y = 5; 7x – 3y = 4 3. 2x + 5y = 12; 5y = 4x + 6