Can someone please check my work for me.

Q: Plot the graph of the equations 2x - 3y = 5 and 4x - 6y = 21 and interpret the result.
A: 6(2x ¨C 3y = 5) = 12x ¨C 18y = 30
3(4x - 6y = 21) = 12x - 18y = 63

12x ¨C 18y = 30
+ 12x - 18y = 63
0 ¡Ù 93

How many solutions does the system of equations below have?

10x – 9y = -10
20x – 18y = -20

To check your work for plotting the graph of the equations 2x - 3y = 5 and 4x - 6y = 21, you need to simplify the equations to their standard form before attempting to graph them.

For the first equation, 2x - 3y = 5, let's rearrange it to isolate y:

2x - 5 = 3y
(2/3)x - (5/3) = y

Now we have the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is (2/3) and the y-intercept is -(5/3).

For the second equation, 4x - 6y = 21, let's rearrange it to isolate y:

4x - 21 = 6y
(2/3)x - (7/3) = y

Again, we have the equation in slope-intercept form, y = mx + b. The slope is (2/3) and the y-intercept is -(7/3).

Now that we have the equations in slope-intercept form, we can plot them on a graph. Remember that the y-intercept is the point where the graph intersects the y-axis, and the slope determines the steepness of the line.

After plotting the lines, you can interpret the result by looking at the intersection point (if any). If the lines intersect at a point, that means there is a solution that satisfies both equations. If the lines are parallel and do not intersect, there is no solution. If the lines are coincident (overlap each other), there are infinitely many solutions.

So, based on your solution of 0 = 93, it seems that you made an error in your calculations. Please double-check your work and recalculate the intersection point.