Question
Evaluate $x,y$ if $\left[\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right]\left[\begin{array}{c}2 x \\ 1\end{array}\right]+2\left[\begin{array}{c}-4 \\ 5\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]$
✓
Answer
$\begin{array}{l}{\left[\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right]\left[\begin{array}{c}2 x \\ 1\end{array}\right]+2\left[\begin{array}{c}-4 \\ 5\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]} \end{array}$
${\left[\begin{array}{c}3 \times 2 x+(-2) \times 1 \\ -1 \times 2 x+4 \times 1\end{array}\right]+\left[\begin{array}{c}-8 \\ 10\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]} $
${\left[\begin{array}{c}6 x-2 \\ -2 x+4\end{array}\right]+\left[\begin{array}{c}-8 \\ 10\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]} $
$ {\left[\begin{array}{c}6 x-2-8 \\ -2 x+4+10\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]} $
$ {\left[\begin{array}{c}6 x-10 \\ -2 x+14\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]}$
$6x - 10 = 8$
$\Rightarrow 6x = 18, x = 3$
$-2x + 14 = 4y$
$\Rightarrow -2x \ 3 + 14 = 4y$
$y=\frac{14-6}{4}$
$=\frac{8}{4}=2$
$x=3, y=2$
${\left[\begin{array}{c}3 \times 2 x+(-2) \times 1 \\ -1 \times 2 x+4 \times 1\end{array}\right]+\left[\begin{array}{c}-8 \\ 10\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]} $
${\left[\begin{array}{c}6 x-2 \\ -2 x+4\end{array}\right]+\left[\begin{array}{c}-8 \\ 10\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]} $
$ {\left[\begin{array}{c}6 x-2-8 \\ -2 x+4+10\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]} $
$ {\left[\begin{array}{c}6 x-10 \\ -2 x+14\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]}$
$6x - 10 = 8$
$\Rightarrow 6x = 18, x = 3$
$-2x + 14 = 4y$
$\Rightarrow -2x \ 3 + 14 = 4y$
$y=\frac{14-6}{4}$
$=\frac{8}{4}=2$
$x=3, y=2$
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
In a race between Mahesh and John, the probability that John will lose the race is 0.54. Find the probability of:
(i) winning of Mahesh
(ii) winning of John
(i) winning of Mahesh
(ii) winning of John
Given a triangle ABC in which $A = (4, -4), B = (0, 5)$ and $C = (5, 10).$ A point P lies on BC such that $BP : PC = 3 : 2,$ Find the length of line segment AP.
→Prove the following identity:
$
\frac{1}{\tan A+\cot A}=\sin A \cos A
$
→$
\frac{1}{\tan A+\cot A}=\sin A \cos A
$
Find the third proportion to the following :
$(x - y)$ and $m (x - y)$
→$(x - y)$ and $m (x - y)$
A book contains 85 pages. A page is chosen at random. What is the probability that the sum of the digits on the page is 8?
Find the equation of a line that has Y-intercept $3$ units and is perpendicular to the line joining $(2, – 3)$ and $(4, 2).$
→Solve the following equation: $7 x+\frac{3}{x}=35 \frac{3}{5}$
→Prove the following Identities:
$
\frac{\operatorname{cosec} A}{\cot A+\tan A}=\cos A
$
→$
\frac{\operatorname{cosec} A}{\cot A+\tan A}=\cos A
$
In the figure, O is the centre of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.
If $A=\left[\begin{array}{cc}-1 & 1 \\ a & b\end{array}\right]$ and $A^2=I$; Find $a$ and $b$
→