Question
Solve the following equations by Cramer’s method.
7x + 3y = 15; 12y – 5x = 39
7x + 3y = 15; 12y – 5x = 39
✓
Answer
$D=\left[\begin{array}{cc}7 & 3 \\ -5 & 12\end{array}\right]=(7 \times 12)-(3 \times-5)=84+15=99$
$D_x=\left[\begin{array}{cc}15 & 3 \\ 39 & 12\end{array}\right]=(15 \times 12)-(3 \times 39)=180-117=63$
$ D_y=\left[\begin{array}{cc}7 & 15 \\ -5 & 39\end{array}\right]=(7 \times 39)-(15 \times-5)=273+75=348 $
$x=\frac{D_x}{D}=\frac{63}{99}=\frac{7}{11} y=\frac{D_y}{D}=\frac{348}{99}=\frac{116}{33} $
$ \therefore(x, y)=\left(\frac{7}{11}, \frac{116}{33}\right)$
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
A bag contains 6 red, 8 black and 4 white balls. A ball is drawn at random. What is the probability that ball drawn is not black?
Show that the points A(-3, 2), B(-5, -5), C(2, -3) and D(4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Hint: Area of a rhombus $=\frac{1}{2}\times(\text{product of its diagonals}).$
→Hint: Area of a rhombus $=\frac{1}{2}\times(\text{product of its diagonals}).$
Write the first five terms of the following sequences whose $n^{th}$ terms are:
$a_n = 2n^2 - 3n + 1.$
→$a_n = 2n^2 - 3n + 1.$
Construct a circle with centre 'O' and radius 4.3 cm. Draw a chord AB of length 5.6 cm. Construct the tangents to the circle at point A and B without using centre.
In the adjoining figure, seg PQ || seg AB. Seg PR || seg BD. Prove that QR || AD.
A bag contains $15$ white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball find the number of black balls in the bag.
→If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes $\frac{6}{5}.$ And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes $\frac{2}{5}.$ Find the fraction.
→From a solid cylinder of height 2.5cm and diameter 4.2cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.$\Big(\text{use}\ \pi=\frac{22}{7}\Big)$
→Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. Find their present ages.
Solve by Cramer’s rule, 3x – 4y = 10; 4x + 3y = 5