How do you solve the system $3 x + z = 13$ $3x + z = 13$ , $2 y + z = 10$ $2y + z = 10$ , $x + y = 1$ $x + y = 1$ ?

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How do you solve the system $3 x + z = 13$ $3x + z = 13$ , $2 y + z = 10$ $2y + z = 10$ , $x + y = 1$ $x + y = 1$ ?

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Answer 1 · 2015-11-21T11:41:42

x=1
y=0
z=10

Explanation:

Write all the equations

$3 \cdot x + z = 13$ $3*x + z = 13$ equation 1
$2 \cdot y + z = 10$ $2*y + z = 10$ equation 2
$x + y = 1$ $x + y =1$ equation 3

The goal is to have at least one equation with only x, y or z

We subtract equation 1 with equation 2 we get:

$3 \cdot x + z - (2 \cdot y + z) = 13 - 10$ $3*x + z -(2*y + z) = 13-10$ ( $e q u a t i o n 1 - e q u a t i o n 2$ $equation 1- equation 2$ )
$3 \cdot x - 2 \cdot y = 3$ $3*x - 2*y = 3$ ( $e q u a t i o n 1 - e q u a t i o n 2$ $equation 1- equation 2$ )

Add equation 3 two times

$3 \cdot x - 2 \cdot y + 2 \cdot (x + y) = 3 + 2 \cdot 1$ $3*x - 2*y + 2*(x+y)= 3 + 2*1$
$5 \cdot x = 5$ $5*x =5$
$x = 1$ $x = 1$

$x + y = 1$ $x + y = 1$ equation 3
$y = 1 - x = 1 - 1 = 0$ $y=1-x=1-1=0$
$y = 0$ $y=0$

$2 \cdot y + z = 10$ $2*y+z=10$
$2 \cdot 0 + z = 10$ $2*0+z=10$
$z = 10$ $z=10$

Check so that this works with the equation system,

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How do you solve the system $3 x + z = 13$ $3x + z = 13$ , $2 y + z = 10$ $2y + z = 10$ , $x + y = 1$ $x + y = 1$ ?

1 Answer

Explanation:

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How do you solve the system $3 x + z = 13$ $3x + z = 13$ , $2 y + z = 10$ $2y + z = 10$ , $x + y = 1$ $x + y = 1$ ?