Question

How do you solve $2x - y = - 19,3x + 4y = 0$?

Answer 1

We are provided with two equations with two variables. Hence the two equations will give two values one for x and y each by equalizing the coefficient of any one variable in both the equations.
By equalizing the coefficient of any one variable we will find the value of x and y.

Complete step-by-step answer:
Let’s discuss how we will solve the two equations;
In the given equations we will equate the coefficients of any one variable be it x or y by multiplying with the reverse coefficient.
Now, we will do the calculation part.
$\Rightarrow 2x - 5y = - 19 \times 3$
$\Rightarrow 3x + 2y = 0 \times 2$
(We have multiplied with 3 and 2 reversely to make the coefficient same)
$\Rightarrow 6x - 15y = - 57$
$\Rightarrow 6x + 4y = 0$
(We have obtained these two equations after equating the coefficients)
(We have obtained these two equations after equating the coefficients)
$\Rightarrow - 19y = - 57$ (After subtracting we have got this equation)
$\Rightarrow y = \dfrac{{ - 57}}{{ - 19}}$ (We have found the value of y)
$\Rightarrow y = 3$ (On substituting the value of y in any of the original given equations to obtain y)
$\Rightarrow 2x - 5 \times 3 = - 19$ (Value of y have been substituted in the original equation)
$\Rightarrow 2x = - 19 + 15$ (Now, we will obtain the value of x as well)
$\Rightarrow x = \dfrac{{ - 4}}{2} = - 2$

We obtain x as -2 and y as 3 after solving the two equations.

Note:
The equation given in the question is generally helpful in solving equations in quantitative aptitude in the problem of ages, percentage, etc. Similarly, used in the consistency and inconsistency form of the equation of the matrix given to us (matrix is a grid of rows and columns), In C programming language we use an array which is also a grid of numbers with two or more than two variables.