Solve by Graphing x+y=-2 , y=x-7

Problem

{[x+y=−2],[y=x−7])

Solution

1. Rewrite the first equation in slope-intercept form y=m*x+b by subtracting x from both sides.

x+y=−2

y=−x−2

2. Identify the slope and y-intercept for the first line y=−x−2

(m_1)=−1

(b_1)=−2

3. Identify the slope and y-intercept for the second line y=x−7

(m_2)=1

(b_2)=−7

4. Graph both lines on the coordinate plane and locate the point where they intersect.

y=−x−2

y=x−7

5. Find the intersection point by setting the two expressions for y equal to each other.

−x−2=x−7

−2*x=−5

x=2.5

6. Substitute the x value back into either equation to find the y value.

y=2.5−7

y=−4.5

Final Answer

(x,y)=(2.5,−4.5)

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