Question

Solve the following simultaneous equations by substitution method.
$2x + 3y = - 4$, $x - 5y = 11$
$A)x = - 1,y = 2$
$B)x = 1,y = - 2$
$C)x = - 1,y = - 2$
$D)x = 1,y = 2$

Answer 1

Hint: If we are given two linear equations then we can solve them in many ways like using elimination method, substitution method and matrix method. We will use the given equations in the substitution method. Where the variables are given as $x,y$

Complete step by step answer:
Given that $2x + 3y = - 4$, $x - 5y = 11$ mark it using the equation $1,2$ respectively.
Let us convert the one equation into any variable form like take the equation two and then $x - 5y = 11 $
$\Rightarrow x = 11 + 5y$
Now applying the values in equation one we get, $2x + 3y = - 4$
$ \Rightarrow 2(11 + 5y) + 3y = - 4$
Using the multiplication, we have $22 + 10y + 3y = - 4$. Further solving with the addition and subtraction operation, we get $22 + 13y = - 4 $
$\Rightarrow 13y = - 26$
$ \Rightarrow y = - 2$ which is the first value.
Now substitute the value in the equation one, we get $2x + 3y = - 4 $
$\Rightarrow 2x + 3( - 2) = - 4 $
$\Rightarrow 2x = - 4 + 6$ again by making use of the basic operations, and hence we get $2x = 2 $
$\Rightarrow x = 1$ (by division)
Hence, we have the two values as $x = 1,y = - 2$ is the answer

So, the correct answer is “Option B”.

Note:
We can solve this question by the elimination method. In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.