Solve the following equations by Cramer’s method. 3 x -2 y =5 2 ;… - Vidyadip

Question

Solve the following equations by Cramer’s method.
$3 x -2 y =\frac{5}{2} ; \frac{1}{3} x +3 y =-\frac{4}{3}$

✓

Answer

$3 x -2 y =\frac{5}{2} \Rightarrow 6 x -4 y =5 $
$ \frac{1}{3} x +3 y =-\frac{4}{3} \Rightarrow \frac{ x +9 y }{3}=-\frac{4}{3} \Rightarrow x +9 y =-4 $
$ D =\left[\begin{array}{cc}6 & -4 \\ 1 & 9\end{array}\right]=(6 \times 9)-(-4 \times 1)=54+4=58$
$ D _{ x }=\left[\begin{array}{cc}5 & -4 \\ -4 & 9\end{array}\right]=(5 \times 9)-(-4 \times-4)=45-16=29$
$ D _{ y }=\left[\begin{array}{cc}6 & 5 \\ 1 & -4\end{array}\right]=(6 \times-4)-(5 \times 1)=-24-5=-29 $
$ x=\frac{D_x}{D}=\frac{1}{2}, y=\frac{D_y}{D}=\frac{(-29)}{58}=\frac{(-1)}{2}$
$ \therefore( x , y )=(1 / 2,-1 / 2)$

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 "3 Marks Question" from P-1 Linear Equations in Two Variables→P-1 Linear Equations in Two Variables — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

A hollow sphere of internal and external diameters $4$ and $8\ cm$ respectively is melted into a cone of base diameter $8\ cm$. Find the height of the cone.

Find the area of $\triangle\text{ABC}$ whose vertices are:
$A(10, -6), B(2, 5)$ and $C(-1, 3)$

The sum of $5^{\text {th }}$ and $9^{\text {th }}$ terms of an A.P. is $30$ . If its $25^{\text {th }}$ term is three times its $8^{\text {th }}$ term, find the A.P.?

A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a -
(1) prime number
(2) multiple of 4
(3) multiple of 11.

The $n ^{\text {th }}$ term of an A.P. is $6 n +2$. Find the common difference.

Express the HCF of 468 and 222 as 468x + 222y where x, y are integers in two different ways.

Find:$9^{th}$ term of the A.P. $\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4}, .....$

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

Find the HCF of the following pairs of integers and express it as a linear combination of them.
506 and 1155

The floor of a rectangular hall is $24\ m$ and breadth $80\ cm$ , will be required to cover the floor of the hall?