Question

Graph the system of equations 8x+8y=64 2x-2y=-4

Answer 1

Answer is attached in the graph.

Step by step

The easiest way to solve these is to graph on an internet or app graphing calculator.

To graph by hand you need to simplify them and arrange in slope intercept form y=mx + b

(#1)

8x + 8y = 64 all are divisible by 8

8/8x + 8/8y = 64/8

Simplify

x + y = 8

Arrange in slope intercept form

subtract x from both sides to isolate y

x - x + y = -x + 8

y = -x + 8

We plot the first point of y intercept of 8 (0,8) and plot the 2nd point by slope of -1/1 or

( 1, -1). Draw your line

(#2)

2x - 2y = -4 are all divisible by 2

2/2x - 2/2y = -4/2

Simplify

x - y = -2

Arrange in slope intercept form

subtract x from both sides to isolate y

x - x - y = -x -2

Simplify

-y = -x -2

Change the signs by multiplying all by -1

y= x +2

We plot the first point of y intercept

of 2 (0, 2) and plot the 2nd point by slope of 1/1 or ( 1, 1). Draw your line

Now you can find the solution is where the lines intersect. At (3, 5)

See my attached graph for your two line equations below

y = x + 2

y = -x + 8

Answer 2

To graph a system of equations, you can first solve each equation for y, and then plot the solutions on the same coordinate plane.

For the first equation, 8x + 8y = 64, we can solve for y by subtracting 8x from both sides, which gives us 8y = 64 - 8x. Then we divide both sides by 8 to get y = (64 - 8x)/8.

For the second equation, 2x - 2y = -4, we can solve for y by adding 2x to both sides, which gives us 2y = 2x - 4.

So the solutions for y in the first equation are:

y = (64 - 8x)/8

and in the second equation are:

y = 2x - 4

We can now plot these two lines on the same coordinate plane. The point of intersection of these two lines will be the solution of the system of equations