Question

What is the -value in the solution to this system of linear equations?y

4 + 5 = −12xy

-2 + 3 = −16xy

Answer 1

The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.

What is a system of linear equations?

Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.

When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.

From the given information:

4x + 5y = -12  --- (1)

-2x + 3y = -16 ----- (2)

From equation (1)

4x+5y+(−5y) = −12 + (−5y)       (Add -5y to both sides)

4x = −5y − 12

Divide both sides by 4

$\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}$

$\mathbf{x= \dfrac{-5}{4}y-3}$

Replacing the value of x in $\mathbf{ \dfrac{-5}{4}y-3}$ into equation (2); we have:

$=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}$

$\mathbf{\dfrac{11}{2}y+6 =-16}$

Simplifying both sides of the equation, we have:

$\mathbf{\dfrac{11}{2}y+6-6 =-16-6}$

$\mathbf{\dfrac{11}{2}y=-22}$

Cross multiply

11y = -44

y = -4

Replace the value of y = -4 into $\mathbf{x= \dfrac{-5}{4}y-3}$

$\mathbf{x= \dfrac{-5}{4}(-4)-3}$

x = 2

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