Question

find x y 2x+3y=4 3y=5​

Answer 1

Answer:

$2x+3y=4,\:3y=5\quad :\quad x=-\frac{1}{2},\:y=\frac{5}{3}$

Step-by-step explanation:

$\begin{bmatrix}2x+3y=4\\ 3y=5\end{bmatrix}$

$\black{\mathrm{Isolate}\:y\:\mathrm{for}\:3y=5:}$

$3y=5$

$\gray{\mathrm{Divide\:both\:sides\:by\:}3}$

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

$\gray{\mathrm{Simplify}}$

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

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

$\begin{bmatrix}2x+3\cdot \frac{5}{3}=4\end{bmatrix}$

$\black{\mathrm{Isolate}\:x\:\mathrm{for}\:2x+3\frac{5}{3}=4:}$

$2x+3\cdot \frac{5}{3}=4$

$\gray{3\cdot \frac{5}{3}=5}$

$2x+5=4$

$\gray{\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}}$

$2x+5-5=4-5$

$\gray{\mathrm{Simplify}}$

$2x=-1$

$\gray{\mathrm{Divide\:both\:sides\:by\:}2}$

$\frac{2x}{2}=\frac{-1}{2}$

$\gray{\mathrm{Simplify}}$

$x=-\frac{1}{2}$

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

$x=-\frac{1}{2},\:y=\frac{5}{3}$