Question
Solve, using cross$-$multiplication $:4x + 6y = 15,3x - 4y = 7$
✓
Answer
Given equation are $4 x+6 y=15$ and $3 x-4 y=7$
Comparing with $\mathrm{a}_1 \mathrm{x}+\mathrm{b}_1 \mathrm{y}+\mathrm{c}_1=0$ and $\mathrm{a}_2 \mathrm{x}+\mathrm{b}_2 \mathrm{y}+\mathrm{c}_2=0$,
We have
$a_1=4, b_1=6, c_1=-15$ and $a_2=3, b_2=-4, c_2=-7$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow x= \frac{6 \times(-7)-(-4) \times(-15)}{4 \times(-4)-3 \times 6}$ and $y=\frac{-15 \times 3-(-7) \times 4}{4 \times(-4)-3 \times 6}$
$ \Rightarrow x=\frac{-42-60}{-16-18}$ and $y=\frac{-45+28}{-16-18}$
$ \Rightarrow x \frac{-102}{-34}$ and $y=\frac{-17}{-34}$
$ \Rightarrow x=3$ and $y=\frac{1}{2}$
Comparing with $\mathrm{a}_1 \mathrm{x}+\mathrm{b}_1 \mathrm{y}+\mathrm{c}_1=0$ and $\mathrm{a}_2 \mathrm{x}+\mathrm{b}_2 \mathrm{y}+\mathrm{c}_2=0$,
We have
$a_1=4, b_1=6, c_1=-15$ and $a_2=3, b_2=-4, c_2=-7$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow x= \frac{6 \times(-7)-(-4) \times(-15)}{4 \times(-4)-3 \times 6}$ and $y=\frac{-15 \times 3-(-7) \times 4}{4 \times(-4)-3 \times 6}$
$ \Rightarrow x=\frac{-42-60}{-16-18}$ and $y=\frac{-45+28}{-16-18}$
$ \Rightarrow x \frac{-102}{-34}$ and $y=\frac{-17}{-34}$
$ \Rightarrow x=3$ and $y=\frac{1}{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If 2x + y = 23 and 4x - y = 19; find the values of x - 3y and 5y - 2x.
Find $x$, if : $\left(\sqrt{\frac{3}{5}}\right)^{x+1}=\frac{125}{27}$
→Simplify:
$(a+b)^2-(a-b)^2$
→$(a+b)^2-(a-b)^2$
$E, F, G,$ and $H$ are the midpoints of the sides of a parallelogram $\text{ABCD}.$Show that the area of quadrilateral $\text{EFGH}$ is half of the area of parallelogram $\text{ABCD}.$
→Construct a right$-$angled triangle in which Side $DE = 6 \ cm$ and $\angle E = 30^\circ , \angle D = 90^\circ $
→Construct a rectangle $\text{ABCD}$, when $AB = 5\ cm$ and $BC = 6.2\ cm.$
→A parallelogram $\text{ABCD}$ has $P$ the mid$-$point of $D c$ and $Q$ a point of Ac such that$CQ =\frac{1}{4} AC . PQ$ produced meets $BC$ at $R$.
Prove that$(i) R$ is the midpoint of $B C(ii) PR =\frac{1}{2} DB$
→Prove that$(i) R$ is the midpoint of $B C(ii) PR =\frac{1}{2} DB$
Use the graphical method to find the value of $k$, if:$(k, -3)$ lies on the straight line $2x + 3y = 1$
→In a quadrilateral $\text{ABCD}, \angle B=90^{\circ}$ and $\angle D=90^{\circ}$.Prove that: $2 A C^2-A B^2=B C^2+C D^2+D A^2$
→The length, breadth, and height of a rectangular solid are in the ratio $6 : 4 :3$. If the total surface area is $1728 \ cm^2$. Find its dimensions.
→