The number of solutions of the system of equations x-y+z=2 2x+y-z=5 4x+y+z=10 is

Question

The number of solutions of the system of equations x-y+z=2 2x+y-z=5 4x+y+z=10 is (A)  ∞  (B)  1  (C)  2  (D)  0

Tardigrade Admin · Accepted Answer

Given system of equations are x-y+z=2 2x+y-z=5 and 4x+y+z=10 Now, A=| beginmatrix 1 -1 1 2 1 -1 4 1 1 endmatrix | =1(1+1)+1(2+4)+1(2-4) =2+6-2 =6≠ 0 Hence, it has unique solution.b

Q. The number of solutions of the system of equations $x - y + z = 2$ $2 x + y - z = 5$ $4 x + y + z = 10$ is

$\infty$

$1$

$2$

$0$

Given system of equations are
$x - y + z = 2$ $2 x + y - z = 5$ and $4 x + y + z = 10$
Now, $A = ∣ ∣ 124 - 1 11 1 - 1 1 ∣ ∣$
$= 1 (1 + 1) + 1 (2 + 4) + 1 (2 - 4)$
$= 2 + 6 - 2$ $= 6 \neq = 0$
Hence, it has unique solution.b

Q. The number of solutions of the system of equations x−y+z=2 2x+y−z=5 4x+y+z=10 is

∞

1

2

0

Given system of equations are x−y+z=2 2x+y−z=5 and 4x+y+z=10 Now, A=∣∣​124​−111​1−11​∣∣​ =1(1+1)+1(2+4)+1(2−4) =2+6−2 =6=0 Hence, it has unique solution.b

Q. The number of solutions of the system of equations $x - y + z = 2$ $2 x + y - z = 5$ $4 x + y + z = 10$ is

$\infty$

$1$

$2$

$0$

Given system of equations are
$x - y + z = 2$ $2 x + y - z = 5$ and $4 x + y + z = 10$
Now, $A = ∣ ∣ 124 - 1 11 1 - 1 1 ∣ ∣$
$= 1 (1 + 1) + 1 (2 + 4) + 1 (2 - 4)$
$= 2 + 6 - 2$ $= 6 \neq = 0$
Hence, it has unique solution.b