Question
Solve the following equations by Cramer’s method.
6x – 3y = –10; 3x + 5y – 8 = 0
6x – 3y = –10; 3x + 5y – 8 = 0
✓
Answer
$\begin{aligned} & 6 x-3 y=-10 \\ & 3 x+5 y=8 \\ & D=\left[\begin{array}{cc}6 & -3 \\ 3 & 5\end{array}\right]=(6 \times 5)-(-3 \times 3)=30+9=39 \\ & D_x=\left[\begin{array}{cc}-10 & -3 \\ 8 & 5\end{array}\right]=(-10 \times 5)-3 \times 8=-50+24=-26 \\ & D_y=\left[\begin{array}{cc}6 & -10 \\ 3 & 8\end{array}\right]=(6 \times 8)-(-10 \times 3)=48+30=78 \\ & x=\frac{D_x}{D}=\frac{-26}{39}=\frac{-2}{3} y=\frac{D_y}{D}=\frac{78}{39}=2 \\ & \therefore(x, y)=\left(-\frac{2}{3}, 2\right)\end{aligned}$
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 the values of k for which the system will have (i) a unique solution, and (ii) no solution.
Is there a value of k for which the system has infinitely many solutions?
→Is there a value of k for which the system has infinitely many solutions?
$2x + ky = 1$
$3x - 5y = 7$
PQ is a chord of length $4.8\ cm$ of a circle of radius $3\ cm$. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP.
→The following table gives the daily income of 50 workers of a factory:
Find the mean, mode and median of the above data.
|
Daily income (in ₹)
|
100-120
|
120-140
|
140-160
|
160-180
|
180-200
|
|
Number of workers
|
12
|
14
|
8
|
6
|
1
|
In the figure 3.36 a rectangle PQRS is inscribed in a circle with centre T.
Prove that, (i) arc PQ ≅ arc SR
(ii) arc SPQ ≅ arc PQR
Prove that, (i) arc PQ ≅ arc SR
(ii) arc SPQ ≅ arc PQR
How many numbers of two digit are divisible by $3$?
→The sum of the radii of two circles is 7cm, and the differece of their circumferences is 8cm. Find the circumferences of the circleas.$\Big[\text{Use }\pi=\frac{22}{7}\Big]$
→Mr. Hariram investment in shares is given below. Find his total investment in shares.
Company A: 200 shares, face value = Rs.100 Premium = Rs. 25
Company B: 500 shares, face value = Rs.100 Market Value = Rs. 200
Company C: 50 shares, face value =Rs 100 Discount =Rs.20
Company A: 200 shares, face value = Rs.100 Premium = Rs. 25
Company B: 500 shares, face value = Rs.100 Market Value = Rs. 200
Company C: 50 shares, face value =Rs 100 Discount =Rs.20
Solve the following quadratic equation by completing the square method.
$m^2-5 m=-3$
→$m^2-5 m=-3$
Very-Short and Short-Answer Questions:Write the number of solutions of the following pair of linear equations:
$x + 2y - 8 = 0,$
$2x + 4y = 16$
→$x + 2y - 8 = 0,$
$2x + 4y = 16$