Simultaneous Linear Equation Problem I am in the eighth standard. I have an examination on linear equations tomorrow. I am stuck in the following problem.
$$ \begin{cases}
2x - 5y = 4,\\
3x - 2y = -16.\end{cases} $$
Find $x$ and $y$. Any help will be appreciated. Thanks in advance.
 A: HINT:
METHOD $1:$ Elimination
Multiply the first equation by $3$ and the second by $2$ and then subtract
METHOD $2:$ Comparison
From the first equation $y=\frac{2x-4}5$ and from the second $y=\frac{3x+16}2$
Equate them to find $x$ 
METHOD $3:$ Substitution
From the first equation $y=\frac{2x-4}5$
Now put this value of $y$ to the second equation
METHOD $4:$ Cross Multiplication
A: In general, if your two simultaneous equations are arranged in this order:
$ax + by = c$ and $dx + ey = f$ where $a,b,c,d,e,f$ are any numbers (some could be negative or even zero) then you can always get the answer by multiplying the first equation by $d$ and the second equation by $a$ (provided neither are zero) and subtracting your two new equations to eliminate all $x$ and leave an equation just in $y$. You then solve it and substitute the value back in either original equation to find $x$. You have to be very careful with minus signs though! 
A: Multiply the first equation by $4$ and then add it with the second equation.
We get the ratio of $x$ and $y$.
Then, substitute $x$ with $y$ in the first equation to get the value of $y$.
After that, use the ratio of $x$ and $y$ to get the value of $x$.
A: There are many methods as one of the answers show. I am just explaining one method.
So you have two equations and two unknowns(x and y). What we are going to do first is to get rid of one of the unknowns.
Suppose we want to get rid of $x$. Note that in the first equation the coefficient of $x$ is 2 and ind second it is 3.We are going to multiply the first equation with coefficient of second and the second with that of first.
So
(eq.1) $\times $ 3 gives
$$6x-15y=12$$
(eq.2) $\times $ 2 gives
$$ 6x-4y=-32$$Now note that coefficient of x in both equations are the same.So when we subtract one equation from the other x will disappear.
We will get
$$-11y=44$$ This will give us $y$ and when we use it one of the equations we will get $x$ also
