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How do you solve $x=-4y$ and $3x+2y=20$?

Last updated date: 17th Jun 2024
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Hint: In this problem we have to solve the given equations i.e., we need to calculate the values of $x$ and $y$ for which the given equations are satisfied. We can observe that the given equation $x=-4y$ is the value of $x$ in terms of $y$. So, we will substitute this value in the second equation which is $3x+2y=20$. Now we will Simplify the equation and convert it into a single variable. After converting the whole equation into a single variable, we will perform some arithmetic operation to solve the equation. After solving the equation, we have the value of one variable and for another variable we will use the given equation $x=-4y$ and calculate the value of another variable.

Complete step by step answer:
Given equations, $x=-4y$ and $3x+2y=20$.
We can observe that the one of the given equations $x=-4y$ is the value of $x$ in terms of $y$. So, substituting this value in the equation $3x+2y=20$, then we will get
$\Rightarrow 3\left( -4y \right)+2y=20$
When we multiply a positive sign with a negative sign, then we will get a negative sign as a result. Hence the above equation is modified as
$\Rightarrow -12y+2y=20$
Simplifying the above equation, then we will get
$\Rightarrow -10y=20$
Dividing the above equation with $-10$ on both sides, then we will get
  & \Rightarrow \dfrac{-10y}{-10}=\dfrac{20}{-10} \\
 & \Rightarrow y=-2 \\
We have the value of $y$ as $-2$. Now we are going to calculate the value of $x$ by substituting $y=-2$ in the given equation $x=-4y$, then we will get
$\Rightarrow x=-4\left( -2 \right)$
Simplifying the above equation, then we will get
$\Rightarrow x=8$

Hence the solution of the given equations $x=-4y$ and $3x+2y=20$ is $x=8$, $y=-2$.

Note: We can also solve the equations by plotting a graph on coordinate system. When we plot the graphs of the equations $x=-4y$ and $3x+2y=20$, the graph will look like below
seo images

From the above graph also, we can observe the solution for the given equations as $x=8$, $y=-2$.