Question

What is the coordinate point of this equation?

Answer 1

( -2, 2)

Explanation:

There are many ways to solve this system of equations, but for this one, I chose graphing. The picture for the graphs are shown below.

1) First, let's graph the first equation since it is already in slope-intercept form. By looking at it and using our knowledge of y = mx + b format (with m as the slope and b as the y-intercept), the slope is -2 and the y intercept is -2. Let's mark (0,-2) on our graph and use our slope of -2 to graph more points and draw a line.

2) Next, let's transform the second equation into y = mx+b format so we can graph it easily. All we need to do is isolate y on the left side like so:

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

3) So, from our work in the previous step, we can do the same thing we did in step 1 and graph
`y = -(1)/(2) x + 1`. Let's mark (0,1) on our graph and use the slope to graph more points and form a line.

4) So, now that we have our graph, we can see that it intersects at (-2,2), therefore that is our solution.

Please don't hesitate to ask any questions!

Answer 2

y = -2x -2

x + 2y = 2

2x + y = -2 } x1

x + 2y = 2 } x2

2x + y = -2 } we eliminate 2x

2x + 4y = 4 } same signs subtract and different add respectively

-3y = -6

-3 -3

y = 2 (x , 2) we reserve

2x + (2) = -2 we take on the first equation and replace 2 on a coordinate for y

2x = -2 - 2

2x = -4

2 2

x = -2 (-2,2)

x y