Question

Solve the system by elimination.
{x+5y-4z=-10
{2x-y+5z=-9
{2x-10y-5z=0

Answer 1

x + 5y - 4z = -10 -->(-2)
2x - y + 5z = -9
-----------------
-2x - 10y + 8z = 20 (result of multiplying by -2)
2x - y + 5z = -9
-----------------add
-11y + 13z = 11

2x - y + 5z = -9 -->(-1)
2x - 10y - 5z = 0
---------------
-2x + y - 5z = 9 (result of multiplying by -1)
2x - 10y - 5z = 0
---------------add
-9y -10z = 9

-11y + 13z = 11 -->(9)
-9y - 10z = 9 --> (-11)
---------------
-99y + 117z = 99 (result of multiplying by 9)
99y + 110z = -99 (result of multiplying by -11)
----------------add
227z = 0
z = 0

now sub 0 in for z
-11y + 13z = 11
-11y + 13(0) = 11
-11y = 11
y = -1

now sub 0 in for z and -1 in for y
x + 5y - 4z = -10
x + 5(-1) - 4(0) = -10
x - 5 = -10
x = -10 + 5
x = -5

lets check it
2x - y + 5z = -9
2(-5) -(-1) + 5(0) = -9
-10 + 1 = -9
-9 = -9 (correct)

x = -5, y = -1, and z = 0