Question

Which graph shows the solution to the system of equations? Solve the system graphically. Click on the graph until the correct solution appears. 2x + 3y = 6 x + y = 4

Answer 1

2x + 3y = 6 → 2x + 3y = 6
x + y = 4 → 3x + 3y = 12
-x = -6
-1 -1
x = 6
x + y = 4
6 + y = 4
- 6 - 6
y = -2
(x, y) = (6, -2)

Answer 2

Answer: Solutions for the value of x and y are given below:

`x=6\\\\y=-2`

Explanation:

since we have given that

2x + 3y = 6

x + y = 4

We need to plot the equation to show the graph.

For first equation:

2x + 3y = 6

put x=0

`0+3y=6\\\\y=(6)/(3)\\\\y=2`

And Put y = 0

`2x=6\\\\x=(6)/(2)\\\\x=3`

So, Coordinates for the above equation are

(0,2) and (3,0)

Similarly, for second equation :

x + y = 4

Put x=0

`y=4\\\\Put\ y=0\\\\x=4`

So, coordinates of the above equation are

(0,4) and (4,0)

So, the graph is shown below:

Now, we need to solve the system graphically,

So, the two equations intersect at (6,-2) in the graph.

so, Solutions for the value of x and y are given below:

`x=6\\\\y=-2`