Question

use the graph to solve the given system of equations by plotting both lines in the point of intersection and moving the dots to the correct location and enter your solution below

Answer 1

Given the system of equations :

`\begin{gathered} x-y=2 \\ 3x+2y=-4 \end{gathered}`

We will use the graph to solve the given system of equations

To draw each line we need two points

So, let two value for x and find the corresponding value of y

For the line : x - y = 2

When x = 0 , y = -2

When x = 2 , y = 0

so, the line will pass through the points ( 0 , -2 ) and ( 2 , 0 )

for the line : 3x + 2y = -4

When x = 0 , y = -2

When x = 2 , y = -5

So, the line will pass through the points ( 0 , -2 ) and ( 2 , -5 )

The graph of the lines will be as shown in the following figures :

The blue line represents the equation : x - y = 2

The red line represents the equation : 3x + 2y = -4

The green dots represents the points used to graph the lines

As shown: the point of intersection between the lines is : (x,y) = ( 0 , -2 )