Question

Using graphs solve the following equations: $ 3x+5y=12;3x-5y+18=0 $ .
A. $ x=-1,y=3 $
B. $ x=-1,y=7 $
C. $ x=-1,y=5 $
D. $ x=-1,y=2 $

Answer 1

Hint: We have been given two equations to solve. We place them on the graph after converting the equations in the form of a function of x. we take the values of x and find the values of y. Then we find the intersecting point of those two lines to find the solution.

Complete step by step answer:
We have been given two equations $ 3x+5y=12;3x-5y+18=0 $ to solve
We find a set of three points for each equation to plot on the graph. Those two lines intersect at a fixed point on the graph and that point is the solution of the equations.
So, for $ 3x+5y=12 $ , we convert it into a function of x.
 $ \begin{align}
  & \Rightarrow 3x+5y=12 \\
 & \Rightarrow y=\dfrac{12-3x}{5} \\
\end{align} $
We take values of x and find y.

x	4	-1	-6
y	0	3	6

Similarly, for $ 3x-5y+18=0 $ , we convert it into a function of x.
 $ \begin{align}
  & \Rightarrow 3x-5y+18=0 \\
 & \Rightarrow y=\dfrac{3x+18}{5} \\
\end{align} $
We take values of x and find y.

x	4	-1	-6
y	6	3	0

Now we plot those points on the graph to get the intersecting point.

We can see the intersecting point is $ \left( -1,3 \right) $ .
Therefore, the solution of the equations is $ x=-1,y=3 $ . The correct option is A.

Note:
 If the intersecting point is hard to understand from the graph then we can draw two perpendicular lines from the point on the main axes. The foot of those perpendicular lines is the coordinates of the points. From that we find the coordinates of the intersecting point.