Question

Solve by Graphing:

2x +2y = -8

y= 2x + 2

Answer 1

Given equations are 2x+2y = -8

Subtract 2x from each side.

2x-2x+2y = -2x-8

Divide to each side by 2.

2y/2 = -2x/2-8/2

y = -x-4

And y = 2x+2

To find coordinate pair substitute x = 0,1,-1 in above equations,

The the points of first equation would be (0,-4),(1,-5),(-1,-3)

Points of second equation would be (0,2),(1,4),(-1,0)

Graph of above equations

Draw the coordinate plane.

Plot the above points.

Connect the above points.

Then the formed lines indicating above equations.

Observe the graph the two lines are intersecting at (-2,-2).

Solution of the given system is x = -2, y = -2.

 

Answer 2

The system of equations are 2x + 2y = - 8 and y = 2x + 2.

Write the equations in slope - intercept form : y = mx + b, where m is slope and b is y - intercept.

The first equation is 2x + 2y = - 8.

x + y = - 4

y = - x - 4.

Compare the equation with slope - intercept form : y = mx + b.

slope = - 1 and y - intercept is - 4.

y - intercept is - 4, so the line crosses the y - axis at (0, - 4).

Using slope find the next point.

Slope = rise/run = - 1/1

Start at point (0, - 4), move 1 unit down and 1 unit right, then plot the point (1, - 5).

The second linear equation is y = 2x + 2.

It is already in slope - intercept form.

Compare the equation with slope - intercept form : y = mx + b.

slope = 2 and y - intercept is 2.

y - intercept is 2, so the line crosses the y - axis at (0, 2)

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, 2), move 2 units up and 1 unit right, then plot the point (1, 4).

Draw the lines through these points.

Graph :

Observe the graph, the solution of the system (x, y ) = (- 2, - 2).