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6.1

6.1. Solving Equations by Graphing. Do Now-. Graph the equation:. 1. y = 1/2x -3. 2. 2x + y = 3. y -intercept: -3. -2x. -2x. Slope: 1/2. y = -2x +3. WORD of the Day !. Function-.

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6.1

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  1. 6.1 • Solving Equations by Graphing

  2. Do Now- Graph the equation: 1. y = 1/2x -3 2. 2x + y = 3 y -intercept: -3 -2x -2x Slope: 1/2 y = -2x +3

  3. WORD of the Day ! Function- A relationship between two variables such that each x-value is paired with no more than one y-value (x values do NOT repeat) Not a Function Function

  4. Investigating Algebra Activity

  5. Vocabulary Systems of linear equations- consists of two or more linear equations using the same variables Solution of a system of linear equations- is an ordered pair that satisfies each equation of the system

  6. Example 1- Check the intersection point Use the graph to solve the system. Then check your solution algebraically. Equation 1 x + 2y = 7 Equation 2 3x – 2y = 5 SOLUTION The lines appear to intersect at the point (3, 2). Substitute3forxand2foryin each equation. CHECK x+ 2y= 7 3x– 2y= 5 3(3) – 2(2) = 5 3+ 2(2) = 7 7 = 7 5 = 5

  7. Example 2- Graph and Check Method SOLVING A LINEAR SYSTEM USING THE GRAPH AND CHECK METHOD STEP 1 - Graph both equations in the same coordinate plane. For ease of graphing, you may want to use slope-intercept form STEP 2 - Estimate the coordinates of the point of intersection STEP 3 - Check the coordinates algebraically by substituting into each equation of the original linear system.

  8. Example 2- Graph and Check Method Solve the linear system: –x + y = –7 x + 4y = –8 Equation2 Equation 1 y = x – 7 y = -1/4x – 2 SOLUTION STEP1 Graph both equations. STEP2 Estimate the point of intersection. The two lines appear to intersect at (4, – 3).

  9. ANSWER Because (4, –3) is a solution of each equation, it is a solution of the linear system. STEP3 Check whether (4, –3) is a solution by substituting 4 for xand –3 for yin each of the original equations. Equation1 Equation2 –x+y= –7 x+4y= –8 –(4) + (–3) = –7 4+ 4(–3) = –8 –7= –7 –8 = –8

  10. ANSWER ANSWER ANSWER 2. ANSWER y = -4x - 3 x – y = 5 –x + 2y = 3 4. 3. 3x + y = 3 2y = 6x +8 2x + y = 4 (2, 3) (-1, 1) (1, 2) (1, 5) Check Point!!!!! Solve the linear system by graphing. Check your solution. 1. –5x + y = 0 5x + y = 10

  11. Example 3- Solve a multi-step problem RENTAL BUSINESS Matt’s business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.

  12. 15 15 15 STEP 1 Write a linear system. Let xbe the number of pairs of skates rented, and let ybe the number of bicycles rented. Equation for number of rentals x + y = 25 Equation for money collected 15x + 30y = 450 STEP2 Graph both equations. x + y = 25 y = -x + 25 15x + 30y = 450 x + 2y = 30 2y = -x +30 y = -1/2x +15

  13. ANSWER Matt’s business rented 20pairs of skates and 5 bicycles. STEP 3 Estimate the point of intersection. The two lines appear to intersect at(20, 5). STEP 4 Check whether (20, 5) is a solution. 15(20) + 30(5) = 450 20+5=25 25 = 25 450 = 450

  14. http://www.ixl.com/math/algebra-1/solve-a-system-of-equations-by-graphinghttp://www.ixl.com/math/algebra-1/solve-a-system-of-equations-by-graphing http://www.ixl.com/math/algebra-1/solve-a-system-of-equations-by-graphing-word-problems

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