Question

Solve the following pair of linear equation by substitution method: 2x-y= -10; -6x+3= 30.

Answer 1

Answer:

$2x-y=-10,\:-6x+3=30\quad :\quad y=1,\:x=-\dfrac{9}{2}$

Step-by-step explanation:

$\begin{bmatrix}2x-y=-10\\ -6x+3=30\end{bmatrix}$

$\black{\mathrm{Isolate}\:x\:\mathrm{for}\:-6x+3=30}$

$-6x+3=30$

$\gray{\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}}$

$-6x+3-3=30-3$

$\gray{\mathrm{Simplify}}$

$-6x=27$

$\gray{\mathrm{Divide\:both\:sides\:by\:}-6}$

$\dfrac{-6x}{-6}=\dfrac{27}{-6}$

$\gray{\mathrm{Simplify}}$

$x=-\dfrac{9}{2}$

$\gray{\mathrm{Subsititute\:}x=-\dfrac{9}{2}}$

$\begin{bmatrix}2\left(-\dfrac{9}{2}\right)-y=-10\end{bmatrix}$

$\black{\mathrm{Isolate}\:y\:\mathrm{for}\:2\left(-\dfrac{9}{2}\right)-y=-10}$

$2\left(-\dfrac{9}{2}\right)-y=-10$

$\gray{\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a}$

$-2\cdot \dfrac{9}{2}-y=-10$

$\gray{2\cdot \dfrac{9}{2}=9}$

$-9-y=-10$

$\gray{\mathrm{Add\:}9\mathrm{\:to\:both\:sides}}$

$-9-y+9=-10+9$

$\gray{\mathrm{Simplify}}$

$-y=-1$

$\gray{\mathrm{Divide\:both\:sides\:by\:}-1}$

$\dfrac{-y}{-1}=\dfrac{-1}{-1}$

$\gray{\mathrm{Simplify}}$

$y=1$

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

$y=1,\:x=-\dfrac{9}{2}$