1 / 10

SOLUTION

–6 x – 9 y = –15. EXAMPLE 1. Multiply one equation , then add. Solve the linear system:. 6 x + 5 y = 19. Equation 1. 2 x + 3 y = 5. Equation 2. SOLUTION. STEP 1. Multiply Equation 2 by –3 so that the coefficients of x are opposites. 6 x + 5 y = 19. 6 x + 5 y = 19.

mika
Download Presentation

SOLUTION

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. –6x – 9y = –15 EXAMPLE 1 Multiply one equation, then add Solve the linear system: 6x + 5y = 19 Equation 1 2x + 3y = 5 Equation 2 SOLUTION STEP 1 Multiply Equation 2 by –3 so that the coefficients of x are opposites. 6x + 5y = 19 6x + 5y = 19 2x + 3y = 5 STEP 2 Add the equations. –4y = 4

  2. EXAMPLE 1 Multiply one equation, then add STEP 3 Solve for y. y = –1 STEP 4 Substitute –1 for yin either of the original equations and solve for x. 2x + 3y= 5 Write Equation 2. 2x + 3(–1) = 5 Substitute–1 for y. 2x + (–3) = 5 Multiply. Subtract –3 from each side. 2x = 8 x = 4 Divide each side by 2.

  3. ? 2(4)+ 3(–1) = 5 ? 6(4) +5(–1)= 19 19 = 19 5 = 5 EXAMPLE 1 Multiply one equation, then add The solution is (4, –1). ANSWER CHECK Substitute 4 for xand –1 for y in each of the original equations. Equation 2 Equation 1 6x+ 5y= 19 2x+ 3y= 5

  4. EXAMPLE 2 Multiply both equations, then subtract Solve the linear system: 4x + 5y = 35 Equation 1 2y = 3x – 9 Equation 2 SOLUTION STEP 1 Arrange the equations so that like terms are in columns. 4x + 5y = 35 Write Equation 1. –3x + 2y = –9 Rewrite Equation 2.

  5. 8x + 10y = 70 –15x +10y = –45 x = 5 EXAMPLE 2 Multiply both equations, then subtract STEP 2 Multiply Equation 1 by 2 and Equation 2 by 5 so that the coefficient of yin each equation is the least common multiple of 5 and 2, or 10. 4x + 5y = 35 –3x + 2y = –9 Subtract: the equations. STEP 3 23x = 115 Solve: for x. STEP 4

  6. ANSWER The solution is (5, 3). EXAMPLE 2 Multiply both equations, then subtract STEP 5 Substitute 5 for xin either of the original equations and solve for y. 4x+ 5y = 35 Write Equation 1. 4(5)+ 5y = 35 Substitute 5 forx. y = 3 Solve for y.

  7. ? 2(3)= 3(5) – 9 ? 4(5)+ 5(3)= 35 ANSWER The solution is (5, 3). 35= 35 6= 6 EXAMPLE 2 Multiply both equations, then subtract Substitute 5 for xand 3 for yin each of the original equations. CHECK Equation 2 Equation 1 2y= 3x– 9 4x+ 5y= 35

  8. 1. 6x – 2y = 1 ANSWER The solution is (–0.5, –2). for Examples 1 and 2 GUIDED PRACTICE Solve the linear system using elimination. –2x + 3y =–5

  9. 2. 2x + 5y = 3 ANSWER The solution is (9, –3). for Examples 1 and 2 GUIDED PRACTICE Solve the linear system using elimination. 3x + 10y =–3

  10. 3x –7y = 5 3. ANSWER The solution is (–10, –5). for Examples 1 and 2 GUIDED PRACTICE Solve the linear system using elimination. 9y =5x + 5

More Related