Question
Solve the following simultaneous equations using Cramer’s rule.
x + 2y = –1; 2x – 3y = 12
x + 2y = –1; 2x – 3y = 12
✓
Answer
$\begin{aligned} & x+2 y=-1 \\ & 2 x-3 y=12 \\ & D=\left[\begin{array}{cc}1 & 2 \\ 2 & -3\end{array}\right]=(1 \times-3)-(2 \times 2)=-3-4=-7 \\ & D_x=\left[\begin{array}{cc}-1 & 2 \\ 12 & -3\end{array}\right]=(-1 \times-3)-(2 \times 12)=3-24=-21 \\ & D_y=\left[\begin{array}{cc}1 & -1 \\ 2 & 12\end{array}\right]=(1 \times 12)-(-1 \times 2)=12+2=14 \\ & x=\frac{D_x}{D}=-\frac{21}{-7}=3 y=\frac{D_y}{D}=\frac{14}{-7}=-2 \\ & \therefore(x, y)=(3,-2) \text { is solution. }\end{aligned}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find $n$ if the given value of $x$ is the $n ^{\text {th }}$ term of the given A.P.
$20,50,75,100, \ldots . . ; x=1000$.
→$20,50,75,100, \ldots . . ; x=1000$.
From the information, prepare the tax invoice for business to customer. (B2C)
Write any name, address, date, etc.
Supplier: M/s _____ Address ______ Date _____.
Invoice No. _______ GSTIN ______ .
Name of products:
(i) Jam bottle ₹ 75,1 piece, Rate of GST $12 \%$, HSN1207
(ii) Honey bottle ₹ 60, 1 piece, Rate of GST $5 \%$, HSN3607
(iii) Perfume bottle ₹ 225, 1 piece, Rate of GST $18 \%$, HSN9319
→Write any name, address, date, etc.
Supplier: M/s _____ Address ______ Date _____.
Invoice No. _______ GSTIN ______ .
Name of products:
(i) Jam bottle ₹ 75,1 piece, Rate of GST $12 \%$, HSN1207
(ii) Honey bottle ₹ 60, 1 piece, Rate of GST $5 \%$, HSN3607
(iii) Perfume bottle ₹ 225, 1 piece, Rate of GST $18 \%$, HSN9319
Find the value of k for which the following systems of equations has unique solution:
$4x - 5y = k, 2x - 3y = 12$
→$4x - 5y = k, 2x - 3y = 12$
A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3m and its height is 3.5m?
In the given figure, ABCD is a quadrilateral in which diagonal $BD = 24\ cm$, $\text{AL}\perp\text{BD}$ and $\text{CM}\perp\text{BD}$ such that $AL = 9\ cm$ and $CM = 12\ cm$. Calculate the area of the quadrilateral.
→In $\triangle\text{ABC},$ given that $AB = AC$ and $\text{BD}\perp\text{AC}.$
Prove that $BC^2 = 2AC \times CD.$
→Prove that $BC^2 = 2AC \times CD.$
A cylindrical vessel of diameter 14cm and height 42cm is fixed symmetrically inside a similar vessel of diameter 16cm and height 42cm. The total space between the two vessels is filled with cork dust for heat insulation purposes. How many cubic centimeters of cork dust will be required?
A ready-made garment shopkeeper gives 5% discount on the dress of Rs. 1000 and charges 5% GST on the remaining amount, then what is the purchase price of the dress for the customer?
How many numbers of two digit are divisible by $3$?
→In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
→$2x + y = 5$
$4x + 2y = 10$