Question

Find the value of (x+y) and (x-y) if 4x+3y=11; 3x+4y=10

Answer 1

Answer:

$\mathrm{x+3y=11,\:3x+4y=10\quad :\quad x=2,\:y=1}$

$\left(2+1\right)\left(2-1\right)=3$

Step-by-step explanation:

$\begin{bmatrix}\mathrm{4x+3y=11\\ \mathrm{3x+4y=10}\end{bmatrix}}$

$\mathrm{Substitute\:x=\frac{11-3y}{4}}$

$\begin{bmatrix}\mathrm{3\times \frac{11-3y}{4}+4y=10}\end{bmatrix}$

$\mathrm{For\:x=\frac{11-3y}{4}}$

$\mathrm{Substitute\:y=1}$

$\mathrm{x=\frac{11-3\cdot \:1}{4}}$

$\mathrm{x=2}$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$\mathrm{x=2,\:y=1}$

*$\mathrm{(x+y)(x-y)}$

$\left(2+1\right)\left(2-1\right)$

$=3\left(2-1\right)$

$=3\times \:1$

$=3$