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Solve the system using the substitution method: 2x-3y+z=10 y+2z=13 z=5

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fa96 | Student, Grade 11 | eNotes Newbie

Posted September 4, 2012 at 5:26 PM via web

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Solve the system using the substitution method:

2x-3y+z=10

y+2z=13

z=5

Tagged with algebra 2, math

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 4, 2012 at 5:31 PM (Answer #1)

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The following system of equations has to be solved:

2x-3y+z=10 ...(1)

y+2z=13 ...(2)

z=5 ...(3)

From (3), z = 5

Substituting z = 5 in (2) gives y + 10 = 13 or y = 3

Substituting z = 5 and y = 3 in (1) gives 2x - 9 + 5 = 10

=> 2x = 14

=> x = 7

The solution of the equation is x = 7, y = 3 and z = 5

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