Question

a)2x-y=5
x-y=2


b)3x-y=3
3x+4Y=30


C)3X+11Y=14
5X+10Y=15

Answer 1

a) $\begin{cases} 2x-y=5 \\ x-y=2 \end{cases}$

$x=y+2$

$2(y+2)-y=5$

$2y+4-y=5$

$y=1$

$x=1+2=3$


b)

$\begin{cases} 3x-y=3 \\ 3x+4y=30 \end{cases}~\Rightarrow~\begin{cases} 3x-y=3 ~~~\times(-1) \\ 3x+4y=30 \end{cases}~\Rightarrow~\begin{cases} -3x+y=-3 \\ 3x+4y=30 \end{cases}$

Somando membro a membro:

$(-3x+y)+(3x+4y)=-3+30$

$5y=27$

$y=\dfrac{27}{5}$

$3x-y=3$

$3x-\dfrac{27}{5}=3$

$3x=3+\dfrac{27}{5}=\dfrac{15+27}{5}=\dfrac{42}{5}$

$x=\dfrac{\dfrac{42}{5}}{3}=\dfrac{42}{15}=\dfrac{14}{3}$


c)

$\begin{cases} 3x+11y=14 \\ 5x+10y=15 \end{cases}~\Rightarrow~\begin{cases} 3x+11y=14 ~~~\cdot(-5) \\ 5x+10y=15 ~~~~\cdot3 \end{cases}~\Rightarrow~\begin{cases} -15x-55y=-70 \\ 15x+30y=45 \end{cases}$

Somando membro a membro:

$(-15x-55y)+(15x+30y)=-70+45$

$-25y=-30$

$y=\dfrac{-30}{-25}$

$y=\dfrac{6}{5}$

$3x+11y=14$

$3x+11\cdot\dfrac{6}{5}=14$

$3x+\dfrac{66}{5}=14$

$3x=14-\dfrac{66}{5}=\dfrac{70-66}{5}=\dfrac{4}{5}$

$x=\dfrac{\dfrac{4}{5}}{3}=\dfrac{4}{15}$