Question

x+y=7 and 2x-3y=11. ​

Answer 1

Answer:

$x+y=7,\:2x-3y=11\quad :\quad y=\frac{3}{5},\:x=\frac{32}{5}$

Step-by-step explanation:

$\begin{bmatrix}x+y=7\\ 2x-3y=11\end{bmatrix}$

$\black[\mathrm{Isolate}\:x\:\mathrm{for}\:x+y=7:}$

$x+y=7$

$\gray{\mathrm{Subtract\:}y\mathrm{\:from\:both\:sides}}$

$x+y-y=7-y$

$\gray{\mathrm{Simplify}}$

$x=7-y$

$\gray{\mathrm{Subsititute\:}x=7-y}$

$\begin{bmatrix}2\left(7-y\right)-3y=11\end{bmatrix}$

$\black{\mathrm{Isolate}\:y\:\mathrm{for}\:2\left(7-y\right)-3y=11:}$

$2\left(7-y\right)-3y=11$

$\gray{\mathrm{Expand}\:2\left(7-y\right):\quad 14-2y}$

$14-2y-3y=11$

$\gray{\mathrm{Add\:similar\:elements:}\:-2y-3y=-5y}$

$14-5y=11$

$\gray{\mathrm{Subtract\:}14\mathrm{\:from\:both\:sides}}$

$14-5y-14=11-14$

$\gray{\mathrm{Simplify}}$

$-5y=-3$

$\gray{\mathrm{Divide\:both\:sides\:by\:}-5}$

$\frac{-5y}{-5}=\frac{-3}{-5}$

$\gray{\mathrm{Simplify}}$

$y=\frac{3}{5}$

$\gray{\mathrm{For\:}x=7-y}$

$\gray{\mathrm{Subsititute\:}y=\frac{3}{5}}$

$x=7-\frac{3}{5}$

$\black{7-\frac{3}{5}}$

$\gray{\mathrm{Convert\:element\:to\:fraction}:\quad \:7=\frac{7\cdot \:5}{5}}$

$=\frac{7\cdot \:5}{5}-\frac{3}{5}$

$\gray{\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}$

$=\frac{7\cdot \:5-3}{5}$

$\gray{7\cdot \:5-3=32}$

$=\frac{32}{5}$

$x=\frac{32}{5}$

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

$y=\frac{3}{5},\:x=\frac{32}{5}$