Solve the system of equations &2 x+5 y=1 &3 x+2 y=7 - Vidyadip

Question

Solve the system of equations $\begin{aligned} &2 x+5 y=1\\ &3 x+2 y=7 \end{aligned}$

✓

Answer

The system of equations can be written in the form AX = B, where
A = $\left[\begin{array}{ll} {2} & {5} \\ {3} & {2} \end{array}\right], X=\left[\begin{array}{l} {x} \\ {y} \end{array}\right]$ and B = $\left[\begin{array}{l} {1} \\ {7} \end{array}\right]$
Now, A = –11 $\neq$ 0, Hence, A is nonsingular matrix and so has a unique solution.
Note that $A^{-1}=-\frac{1}{11}\left[\begin{array}{cc} {2} & {-5} \\ {-3} & {2} \end{array}\right]$
Therefore X = A^–1B = –$\frac{1}{11}\left[\begin{array}{cc} {2} & {-5} \\ {-3} & {2} \end{array}\right]\left[\begin{array}{l} {1} \\ {7} \end{array}\right]$
i.e., $\left[\begin{array}{l} {x} \\ {y} \end{array}\right]=-\frac{1}{11}\left[\begin{array}{c} {-33} \\ {11} \end{array}\right]=\left[\begin{array}{c} {3} \\ {-1} \end{array}\right]$
Hence, x = 3, y = – 1

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks" from Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write whether f : R → R, given by $\text{f(x)}=\text{x}+\sqrt{\text{x}^2},$ is one-one, many-one, onto or into.

$\text{Find}\ \lambda\ \text{and}\ \mu\ \text{if}\ (2\hat{i}+6\hat{j}+27\hat{k})\times(\hat{i}+\lambda\hat{j}+\mu\hat{k})=\vec{0}.$

Verify that the function $y=e^{x}(a \cos x+b \sin x)$ (implicit or explicit) is a solution of the differential equation $\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0$

Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?

If G denots the centroid of $\triangle\text{ABC}$, then write the value of $\overrightarrow{\text{GA}}+\overrightarrow{\text{GB}}+\overrightarrow{\text{GC}}$.

In the following matrix equation use elementary operation R₂ → R₂ + R₁ and the equation thus obtained:
$\begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 2 & -1 \end{bmatrix}\begin{bmatrix} 8 & -3 \\ 9 & -4 \end{bmatrix}$

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\vec{\text{a}}.\vec{\text{b}}=6,|\vec{\text{a}}|=3$ and $\big|\vec{\text{b}}\big|=4.$ write the projection of $\vec{\text{a}}$ on $\vec{\text{b}}.$

Evaluate the following:
$\tan^{-1}\Big(-\frac{1}{\sqrt3}\Big)+\cot^{-1}\Big(\frac{1}{\sqrt3}\Big)+\tan^{-1}\Big(\sin\Big(-\frac{\pi}{2}\Big)\Big)$

Verify that the function y = e^-3x is a solution of the differential equation $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}$ - 6y = 0

Two tailors, A and B, earn ₹ 300 and ₹ 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.