Question

How do I solve this using the substitution method 3x+2y=9 x-5y=4

Answer 1

$\bf \begin{cases} 3x+2y=9\\ x-5y=4 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{solving the 2nd equation for "y"}}{x-5y = 4\implies x-4-5y=0}\implies x-4=5y\implies \cfrac{x-4}{5}=y \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{3x+2\left(\cfrac{x-4}{5} \right) = 9}\implies 3x+\cfrac{2(x-4)}{5}=9 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5\left( 3x+\cfrac{2(x-4)}{5} \right)=5(9)}\implies 15x+2(x-4)=45$

$\bf 15x+2x-8=45\implies 17x-8=45\implies 17x=53\implies \boxed{x=\cfrac{53}{17}} \\\\\\ \stackrel{\textit{we know that}}{\cfrac{x-4}{5}=y}\implies \cfrac{\left(\frac{53}{17} -4 \right)}{5}=y\implies \cfrac{\left(\frac{53-68}{17} \right)}{5}=y\implies \cfrac{~~\frac{-15}{17}~~}{5}=y \\\\\\ \cfrac{~~\frac{-15}{17}~~}{\frac{5}{1}}=y\implies \cfrac{-15}{17}\cdot \cfrac{1}{5}=y\implies \boxed{-\cfrac{3}{17}=y} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \left( \frac{53}{17}~~,~~-\frac{3}{17} \right)~\hfill$

Answer 2

Answer: x = 57/17

y = - 3/17

Step-by-step explanation:

The given system of equations is expressed as

3x + 2y = 9 - - - - - - - - - - - - - -1

x - 5y = 4 - - - - - - - - - - - - - - -2

From equation 2, we would make x the subject of the formula by adding 5y to the left hand side and the right hand side of the equation. It becomes

x - 5y + 5y = 4 + 5y

x = 4 + 5y

Substituting x = 4 + 5y into equation 1, it becomes.

3(4 + 5y) + 2y = 9

12 + 15y + 2y = 9

15y + 2y = 9 - 12

-7y = - 3

y = - 3/17

Substituting y = - 3/17 into equation x = 4 + 5y, it becomes

x = 4 + 5 × - 3/17

x = 4 - 15/17

x = (68 - 15)/17

x = 53/17