Question

-2x -9y = -25
-4x -9y = -23
Please help find (x,y)

Answer 1

x = -1

y = 3

Explanation:

Given:

`\begin{bmatrix}-2x-9y=-25\\ -4x-9y=-23\end{bmatrix}`

Solve:

`\mathrm{Substitute\:}x=-(-25+9y)/(2)`

`\begin{bmatrix}-4\left(-(-25+9y)/(2)\right)-9y=-23\end{bmatrix}`

`\mathrm{Simplify}`

`\begin{bmatrix}9y-50=-23\end{bmatrix}`

`\mathrm{For\:}x=-(-25+9y)/(2)`

`\mathrm{Substitute\:}y=3`

`x=-(-25+9\cdot \:3)/(2)`

`\mathrm{Simplify}`

`x=-1`

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=-1,y=3`

~Lenvy~

Answer 2

Hii !

We can find the value of x and y by using two simple methods, which are as follows -

1. The substitution method is the process of solving the equation to find the variable value, and the value is substituted in the other equation.
2. The elimination method is the process of eliminating the variables in the equation so that the system of the equation can be left as the function of a single variable.

P.S - There are five methods to solve a system of linear equations in two variables in general. Those methods are -

• Graphical Method
• Substitution Method
• Croiss Multiplication Method
• Elimination Method
• Determinant Method

But I will be solving the given linear equations by using the above 2 methods because in the question it's not particularly mentioned and secondly the methods I'll be solving the question with, are considered more in contrast to rest of the methods (from my pov).

So let's start solving,

First we will use th substitution method. In the substitution method first we work by substituting one y-value with the other. To put it simply, the method involves finding the value of the x-variable in terms of the y-variable.

-2x -9y = -25 ---- (i)

-4x -9y = -23 ---- (ii)

Finding the value of x in (i),

=> -2x -9y = -25

=> -2x = -25 + 9y

=> x = -25 + 9y/-2

or we can also write it as,

=> x = 25 - 9y/2 ----(iii)

Finding the value of x in (ii),

=> -4x -9y = -23

=> -4x = -23 + 9y

=> x = -23 + 9y/-4

or we can also write it as,

=> x = 23 - 9y/4 ----(iv)

Now equating the equations (iii) and (iv),

=> 25 - 9y/2 = 23 - 9y/4

=> 4(25 - 9y) = 2(23 - 9y)

=> 100 - 36y = 46 - 18y

=> 36y - 18y = 100 - 46

=> 18y = 54

=> y = 54/18

=> y = 3

Finding the value of x by taking either equation (iii) or (iv),

=> x = 23 - 9(3)/4

=> x = 23 - 27/4

=> x = -4/4

=> x = -1

_____________________________

Using the elimination method, In this method we simply add or subtract the equations, in accordance with the sign they require to eliminate any one value (of x and y).

Here, in this question we will subtract equation (i) and (ii) to eliminate 9y,

-2x -9y = -25

(-) -4x -9y = -23

(+) (+) = (+)

_____________

=> 2x = -2

=> x = -1

Hence, y = 3.

Therefore, the value of x = -1 and y = 3.