Question

How do you solve the system of equations \[-2x-2y=-4\] and \[2x+3y=9\]?

Answer 1

Hint: We will use the substitution method to solve these equations, for this we can first find the value of one variable by eliminating the other, this can be done by adding or subtracting equations from one another. Sometimes we first have to multiply an equation by a constant number so that we can eliminate a variable by adding or subtracting. After this step, we substitute the value in any of the equations to find another variable.

Complete step by step answer:
The given equations are,
\[-2x-2y=-4\]- - - - - (1)
\[2x+3y=9\]- - - - - (2)
From the given two equations we can see that the coefficient of $x$ in the equations is $-2$ and $2$ respectively. So, we can easily eliminate $x$ by simply adding the given two equations.
We add equation (1) and equation (2), we get
\[-2x-2y+2x+3y=-4+9\]
\[\Rightarrow y=5\]- - - - - (3)
Substitute this value in equation (2), we get
\[\begin{align}
  & \Rightarrow 2x+3\times 5=9 \\
 & \Rightarrow 2x+15=9 \\
\end{align}\]
Subtracting 15 from both sides of the equation, we get
\[\begin{align}
  & \Rightarrow 2x+15-15=9-15 \\
 & \Rightarrow 2x=-6 \\
\end{align}\]
Dividing both sides by 2, we get
\[\Rightarrow \dfrac{2x}{2}=\dfrac{-6}{2}\]
\[\therefore x=-3\]- - - - - (4)
From (3) and (4), the solution of the equation is \[(-3,5)\] .

Note: There are many methods to solve two-variable linear equations, like the determinant method, substitution method etc. For this question to solve linear equations in two variables, we used the substitution method. Linear equations in two variables can easily be solved by the substitution method, but you should avoid making any calculation mistakes. Think about how to eliminate one of the variables that are given in the equations.