If the system of linear equations $x-2 y+z=-4 $ ; $2 x+\alpha y+3 z=5 $ ; $3 x-y+\beta z=3$ has infinitely many solutions, then $12 \alpha+13 \beta$ is equal to
If the system of linear equations $x-2 y+z=-4 $ ; $2 x+\alpha y+3 z=5 $ ; $3 x-y+\beta z=3$ has infinitely many solutions, then $12 \alpha+13 \beta$ is equal to
- [JEE MAIN 2024]
- A
$60$
- B
$64$
- C
$54$
- D
$58$
Similar Questions
The values of $\mathrm{m}, \mathrm{n}$, for which the system of equations
$ x+y+z=4 $
$ 2 x+5 y+5 z=17 $
$ x+2 y+m z=n$
has infinitely many solutions, satisfy the equation :
The values of $\mathrm{m}, \mathrm{n}$, for which the system of equations
$ x+y+z=4 $
$ 2 x+5 y+5 z=17 $
$ x+2 y+m z=n$
has infinitely many solutions, satisfy the equation :
- [JEE MAIN 2024]
Consider the following system of questions $\alpha x+2 y+z=1$ ; $2 \alpha x+3 y+z=1$ ; $3 x+\alpha y+2 z=\beta$ . For some $\alpha, \beta \in R$. Then which of the following is NOT correct.
Consider the following system of questions $\alpha x+2 y+z=1$ ; $2 \alpha x+3 y+z=1$ ; $3 x+\alpha y+2 z=\beta$ . For some $\alpha, \beta \in R$. Then which of the following is NOT correct.
- [JEE MAIN 2023]
Find values of $\mathrm{k}$ if area of triangle is $4$ square units and vertices are $(\mathrm{k}, 0),(4,0),(0,2)$
Find values of $\mathrm{k}$ if area of triangle is $4$ square units and vertices are $(\mathrm{k}, 0),(4,0),(0,2)$
For the system of linear equations $a x+y+z=1$, $x+a y+z=1, x+y+a z=\beta$, which one of the following statements is NOT correct ?
For the system of linear equations $a x+y+z=1$, $x+a y+z=1, x+y+a z=\beta$, which one of the following statements is NOT correct ?
- [JEE MAIN 2023]
The value of a for which the system of equations ; $a^3x + (a +1)^3 y + (a + 2)^3 \, z = 0$ ,$ax + (a + 1) y + (a + 2)\, z = 0$ & $x + y + z = 0$ has a non-zero solution is :
The value of a for which the system of equations ; $a^3x + (a +1)^3 y + (a + 2)^3 \, z = 0$ ,$ax + (a + 1) y + (a + 2)\, z = 0$ & $x + y + z = 0$ has a non-zero solution is :