The value of x and y , if the system of linear equations is 2 x - y = 2 and 3 x + 4 y = 3 is:

Question

The value of $x$ and $y$ , if the system of linear equations is $2 x - y = 2$ and $3 x + 4 y = 3$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $x = 1, y = 0$

Explanation:

Given,

$2 x - y = 2$

$3 x + 4 y = 3$

The coefficient matrix is

$A = [\begin{matrix} 2 & - 1 \\ 3 & 4 \end{matrix}]$

$B = [\begin{matrix} 2 \\ 3 \end{matrix}], X = [\begin{matrix} x \\ y \end{matrix}]$

Now, $| A |$ $= 2 (4) - (- 1) (3) = 8 + 3 = 11$

$adj (A) = [\begin{matrix} 4 & 1 \\ - 3 & 2 \end{matrix}]$

Therefore, $A^{- 1} = \frac{1}{11} [\begin{matrix} 4 & 1 \\ - 3 & 2 \end{matrix}]$

Hence, $X = A^{- 1} B$

$[\begin{matrix} x \\ y \end{matrix}] = \frac{1}{11} [\begin{matrix} 4 & 1 \\ - 3 & 2 \end{matrix}] [\begin{matrix} 2 \\ 3 \end{matrix}] = \frac{1}{11} [\begin{matrix} 8 + 3 \\ - 6 + 6 \end{matrix}]$

Thus, $x = \frac{11}{11} = 1, y = \frac{0}{11} = 0$

Hence, $x = 1, y = 0$

Solution

Q.
The value of $x$ and $y$ , if the system of linear equations is $2 x - y = 2$ and $3 x + 4 y = 3$ is:

1 $x = 1, y = 0$

2 $x = 1, y = - 1$

3 $x = 0, y = 1$

4 $x = - 1, y = - 1$

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Solution

Q. The value of x and y, if the system of linear equations is 2x-y=2 and 3x+4y=3 is:

1 x=1, y=0

2 x=1, y=-1

3 x=0, y=1

4 x=-1, y=-1