Question

Graph the system of equation, then find the solution and check the answer.

Answer 1

Given the system of equations:

`\begin{gathered} y=-(2)/(3)x+3 \\ y=2x-5 \end{gathered}`

The equations represents the graph of the lines

To graph a line we need two points

Substitute with two value of x then find y

For the first equation:

`y=-(2)/(3)x+3`

When x = 0 , y = 3

When x = 3 , y = 1

So, the line passing through the points ( 0 , 3 ) and ( 3 , 1 )

The following image represents the graph of the first equation:

For the second equation:

`y=2x-5`

When x = 0 , y = -5

When x = 2 , y = -1

So, the line passing through the points ( 0 , -5 ) and (2 , -1)

The following image represents the line of the second equation .

Now, we will make the two lines on the same graph to find the solution of the system of equations:

As shown, the point of intersection is (3 , 1)

So, the solution of the system = ( 3 , 1 )

To check the answer, substiute with the point (3 , 1 ) at both equations:

So, for the first equation:

when x = 3

`y=-(2)/(3)\cdot3+3=-2+3=1\text{ (true)}`

For the second equation:

when x = 3

`y=2\cdot3-5=6-5=1\text{ (true)}`