Question

How do you solve the system of equations $-4x+7y=20$ and $y=3x+15$ ?

Answer 1

Hint: In this question we have been asked to solve the given system of equations $-4x+7y=20$ and $y=3x+15$. For doing that we will substitute the value of “y” from y=3x+15 into -4x+7y=20.

Complete step by step solution:
Now considering from the question we have been asked to solve the given system of equations $-4x+7y=20$ and $y=3x+15$.
For doing that we will substitute the value of “y” from y=3x+15 into -4x+7y=20 and then perform basic arithmetic simplifications or operations in order to simplify it for the value of “x”.
So by doing the substitution we will have $ -4x+7\left( 3x+15 \right)=20$ .
Now we will perform basic arithmetic simplifications or operations and reduce or simplify this expression in order to get the value of “x”. After doing that we will have $\begin{align}
  & \Rightarrow -4x+7\left( 3x+15 \right)=20 \\
 & \Rightarrow -4x+21x+105=20 \\
 & \Rightarrow 17x=20-105 \\
 & \Rightarrow 17x=-85 \\
 & \Rightarrow x=\dfrac{-85}{17} \\
& \Rightarrow x=-5 \\
\end{align}$
By substituting this value of “x” in y=3x+15 we will have
 $\begin{align}
  & \Rightarrow y=3\left( -5 \right)+15 \\
 & \Rightarrow y=0 \\
\end{align}$
Therefore we can conclude that the solution for the given system of equations $-4x+7y=20$ and $y=3x+15$ is $x=-5,y=0$ that is $\left( -5,0 \right)$ .
The graph of this system of equations will look like:

Note: While answering questions of this type we should be sure with the calculations we perform and the concepts we apply in order to get an appropriate answer or conclusion. We can also solve this question alternatively using the graph which we had seen before for plotting the graph we need to get the x and y intercepts of the both the given equations. After plotting the point of intersection will be the solution. The intercepts of the equation y=3x+15 are (-5,0) and (0,15). Similarly for -4x+7y=20 the intercepts will be given as (-5,0) and (0,20/7). As we can see that they intersect at (-5,0).