Solve each system of equation by grpahing?

3. y=-3x+6
2y=10x-36

4. y=-x-9
3y=5x+5

#3

since one equation tells us that y = -3x+6, use it in the other equation:

2y = 10x-36
2(-3x+6) = 10x-36
-6x+12 = 10x-36
-16x = -48
x = 3

Do #4 the same way

To solve each system of equations by graphing, we need to plot both equations on a coordinate plane and find the point of intersection.

Let's start with the first system of equations:

1. y = -3x + 6
2. 2y = 10x - 36

To graph the first equation, we can start by finding two coordinate points. You can choose any values for x and substitute them into the equation to find the corresponding y values. Let's select x = 0 and x = 2:

For x = 0:
y = -3(0) + 6
y = 6

So, we have the coordinate point (0, 6).

For x = 2:
y = -3(2) + 6
y = 0

So, we have the coordinate point (2, 0).

Now, let's graph the second equation. To do this, let's rearrange the equation to solve for y.

2y = 10x - 36
Divide both sides by 2:
y = 5x - 18

Using the same method, let's find the coordinate points for this equation:

For x = 0:
y = 5(0) - 18
y = -18

So, we have the coordinate point (0, -18).

For x = 2:
y = 5(2) - 18
y = -8

So, we have the coordinate point (2, -8).

Now, we can plot these points on a coordinate plane and draw a line connecting them. The point where the two lines intersect will be the solution to the system of equations.

Now let's move on to the second system of equations:

3. y = -x - 9
4. 3y = 5x + 5

To find the coordinate points for the first equation, we can select values for x and solve for y. Let's choose x = 0 and x = 2:

For x = 0:
y = -(0) - 9
y = -9

So, we have the coordinate point (0, -9).

For x = 2:
y = -(2) - 9
y = -11

So, we have the coordinate point (2, -11).

Now, let's rearrange the second equation to solve for y:

3y = 5x + 5
Divide both sides by 3:
y = (5/3)x + 5/3

Using the same method, let's find the coordinate points for this equation:

For x = 0:
y = (5/3)(0) + 5/3
y = 5/3

So, we have the coordinate point (0, 5/3).

For x = 2:
y = (5/3)(2) + 5/3
y = 5/3 + 5/3
y = 10/3

So, we have the coordinate point (2, 10/3).

Now, plot these points on a coordinate plane and draw a line connecting them. The point where the two lines intersect will be the solution to the system of equations.