Question

What is the solution of the system. Use the substution method. 3x+2y=11, x-2=-4y

Answer 1

Answer:

$x=\frac{10}{3}$ and $y=\frac{1}{2}$

Step-by-step explanation:

• To use the substitution method, we should take one of the equations, and obtain an expression for one of the variables from this equation. Let's take the first one: 3x-2y = 11. We obtain an expression for x (it could be for y as well):  3x = 11 + 2 y ⇒ $x=\frac{11}{3}+\frac{2}{3} \times{y}$.
• Now, we should replace the expression obtain for x in the first equation, on the second equation, as follow

• $x-2=4y$⇒ $(\frac{11}{3}+\frac{2}{3}\times{y})-2=4\times{y}$
• Then rearranging terms $\frac{11}{3}-2=4\times{y}-\frac{2}{3}\times{y}$
• This expression results in $y=\frac{1}{2}$
• Finally, using the firs equation, in which we obtained an expression from x, $x=\frac{11}{3}-\frac{2}{3} \times{y}$, we replace y=1/2 and get $x=\frac{11}{3}- \frac{2}{3}\times{\frac{1}{2} }$, then $x=\frac{10}{3}$