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Use addition to eliminate a variable

Learn how to solve linear systems of equations by eliminating variables using addition or subtraction. Examples and step-by-step solutions provided.

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Use addition to eliminate a variable

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  1. Add the equations to 2x + 3y = 11 eliminate one variable. –2x + 5y = 13 EXAMPLE 1 Use addition to eliminate a variable Solve the linear system: 2x + 3y = 11 Equation 1 –2x + 5y = 13 Equation 2 SOLUTION STEP 1 STEP 2 Solve fory. 8y =24 y =3

  2. ANSWER The solution is(1, 3). EXAMPLE 1 Use addition to eliminate a variable STEP 3 Substitute 3 for yin either equation and solve for x. 2x + 3y = 11 Write Equation 1 2x + 3(3)= 11 Substitute3for y. x = 1 Solve for x.

  3. ? ? 2(1)+ 3(3)= 11 2(1)+ 5(3)= 13 EXAMPLE 1 Use addition to eliminate a variable CHECK Substitute 1 for xand 3 foryin each of the original equations. 2x + 3y= 11 2x + 5y= 13 11= 11 13= 13

  4. Subtract the equations to 4x + 3y = 2 eliminate one variable. 5x + 3y = –2 EXAMPLE 2 Use subtraction to eliminate a variable Solve the linear system: 4x + 3y = 2 Equation 1 5x + 3y = –2 Equation 2 SOLUTION STEP 1 STEP 2 Solve forx. – x = 4 x = 4

  5. ANSWER The solution is (–4, 6). EXAMPLE 2 Use subtraction to eliminate a variable STEP 3 Substitute4 for x in either equation and solve for y. 4x+ 3y = 2 Write Equation 1. 4(–4)+ 3y = 2 Substitute –4 for x. y = 6 Solve fory.

  6. 3x + 4y = 14 Add the equations. 5x = 10 Solve for x. x = 2 EXAMPLE 3 Arrange like terms Solve the linear system: 8x – 4y = –4 Equation 1 4y = 3x + 14 Equation 2 SOLUTION Rewrite Equation 2 so that the like terms are arranged in columns. STEP 1 8x –4y = –4 8x – 4y = –4 4y = 3x + 14 STEP 2 STEP 3

  7. ANSWER The solution is (2, 5). EXAMPLE 3 Arrange like terms STEP 4 Substitute 2 forx in either equation and solve for y. 4y = 3x + 14 Write Equation 2. 4y = 3(2)+ 14 Substitute 2 for x. y = 5 Solve for y.

  8. ANSWER (–1, –3) for Example 1,2 and 3 GUIDED PRACTICE Solve the linear system: 1. 4x – 3y = 5 ` –2x + 3y = –7

  9. – 5x – 6y = 8 ANSWER (2, –3) for Example 1,2 and 3 GUIDED PRACTICE Solve the linear system: 2. 5x + 2y = 4

  10. – 3x + 4y = 1 (5, 4) ANSWER for Example 1,2 and 3 GUIDED PRACTICE Solve the linear system: 3. 6x – 4y = 14

  11. ANSWER (1, 1) for Example 1,2 and 3 GUIDED PRACTICE Solve the linear system: 4. 7x – 2y = 5 7x – 3y = 4

  12. 2y 3x + 6 = ANSWER (–2, 0) for Example 1,2 and 3 GUIDED PRACTICE Solve the linear system: 5. 3x + 4y = –6

  13. 5y 4x + 6 = ANSWER (1, 2) for Example 1,2 and 3 GUIDED PRACTICE Solve the linear system: 6. 2x + 5y = 12

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