Please help!!!!

Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this.

6x - 2y = 2,
9x - 3y = 1

My answer:

Equation 1
X-intercept y=intercept
6x - 2y = 2 6x - 2y = 2

6x - 2(0) = 2 6(0) - 2y = 2

6x - 0 = 2 0 -2y = 2

6x = 2 -2y = 2
6x/6 =2/6 -2y/2 = 2/2
x= 0.75 y = -1

Equation 2

9x - 3y = 1 9x - 3y = 1

9x - 3(0) = 1 9(0) - 3y = 1

9x - 0 = 1 0 - 3y = 1

9x = 1 -3y = 1
9x/9 =1 -3y/3 = 1/3
x= 1/9 y = -1/3
x= 0.9 y= -0.25

It is not clear what you are doing. Rewrite the two equations as follows

18x - 6y = 6
18x - 6y = 2

The two equations are incompatible, and would graph as separate parallel lines.

There is no solution.

-2x+7y=0

can someone help me plz :))

To solve the system of equations graphically, you can plot the equations on a graph and find their point of intersection. This point represents the solution to the system.

For the first equation, 6x - 2y = 2, we can rearrange it to solve for y: y = 3x - 1.

For the second equation, 9x - 3y = 1, we can also rearrange it to solve for y: y = 3x - 1/3.

Now you can plot both equations on the same graph. Choose some x-values and calculate the corresponding y-values for each equation. Then plot the points and draw the lines connecting them.

For the first equation, when x = 0, y = -1 (from y = 3(0) - 1). When x = 1/2, y = 1/2 (from y = 3(1/2) - 1). When x = 1, y = 2 (from y = 3(1) - 1).

For the second equation, when x = 0, y = -1/3 (from y = 3(0) - 1/3). When x = 1/2, y = -1/6 (from y = 3(1/2) - 1/3). When x = 1, y = 2/3 (from y = 3(1) - 1/3).

Now plot these points on a graph and draw the lines connecting them. The point where the two lines intersect is the solution to the system. In this case, the lines intersect at approximately (0.75, -1).

To check the solution, substitute the values of x and y into the original equations:

For the first equation: 6(0.75) - 2(-1) = 4.5 + 2 = 6, which is equal to 2. So the solution satisfies the first equation.

For the second equation: 9(0.75) - 3(-1) = 6.75 + 3 = 9.75, which is not equal to 1. So the solution does not satisfy the second equation.

Since the solution does not satisfy both equations, this system has no solution.

Therefore, the solution to the system of equations 6x - 2y = 2 and 9x - 3y = 1 is no solution.