Question

Solve the following system of equations graphically.

y = 2x - 3
x + y = 3

What is the solution set?

{(2, 1)}
{(1, 2)}
{(-1, -2)}
{(-2, -1)}

Answer 1

(2,1)

I first used substitution to get my answer and then used graphing to check. You can easily get a graphing equation by rearranging the second equation.

Answer 2

(2,1)

Explanation:

Let us graph our first equation

y = 2x - 3

Bring y to the right hands side and 3 to the left hand side of = we get

2x-y=3

Diving each term of the equation by 3 we get

`(2x)/(3)-(y)/(3)=(3)/(3)\\(x)/((3)/(2))+(y)/(-3)=1`

Hence we have converted our equation into intercept form, in x intercept is
`(3)/(2)` and y intercept is -3.

Now we mark the two points are as
`((3)/(2),0)` and (0,-3)

Shown as red line in attachment.

x + y = 3

Dividing both sides by 3

`(x)/(3)+(y)/(3)=1`

Hence our x and y intercepts are 3. Thus we plot coordinates (3,0) and (0,3) and join them together to graph our line.In attachment it is shown in as blue line.

Please refer to the image in the attachment. The two lines intersect at (2,1)

This is our solution.