Question

Solve the following system of equations.
x-2y=9
x+5y=-12
Find the x and y intercepts

Answer 1

No, please try again

Answer 2

You sure?

Answer 3

To solve the system of equations:

1) x - 2y = 9
2) x + 5y = -12

We can use the elimination method. Adding the two equations together, we get:

x - 2y + x + 5y = 9 - 12
2x + 3y = -3

Now we can isolate x:

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

Now we substitute this value of x into one of the original equations. Let's use the first equation:

(-3 - 3y) / 2 - 2y = 9
-3 - 3y - 4y = 18
-7y = 21
y = -3

Now we can substitute this value of y back into the equation for x:

x = (-3 - 3(-3)) / 2
x = (-3 + 9) / 2
x = 6 / 2
x = 3

Therefore, the solution to the system of equations is x = 3, y = -3.

To find the x-intercept, set y = 0 in either of the original equations:

x = 9, so the x-intercept is at (9, 0).

To find the y-intercept, set x = 0 in either of the original equations:

-2y = 9
y = -4.5, so the y-intercept is at (0, -4.5).

Answer 4

Let's solve the system of equations again:

1) x - 2y = 9
2) x + 5y = -12

To eliminate x, we can add the two equations:

x - 2y + x + 5y = 9 - 12
2x + 3y = -3
2x = -3 - 3y
x = (-3 - 3y)/2

Now we substitute x back into the first equation:

(-3 - 3y)/2 - 2y = 9
-3 - 3y - 4y = 18
-7y = 21
y = -3

Now we substitute y = -3 back into the equation for x:

x = (-3 - 3(-3))/2
x = (-3 + 9)/2
x = 6/2
x = 3

Therefore, the solution to the system of equations is x = 3, y = -3.

To find the x-intercept, set y = 0 in the first equation:

x = 9, so the x-intercept is at (9, 0).

To find the y-intercept, set x = 0 in the first equation:

-2y = 9
y = -4.5, so the y-intercept is at (0, -4.5).

Answer 5

I apologize for the error in my previous responses. Let's solve the system of equations again to find the correct solution:

1) x - 2y = 9
2) x + 5y = -12

To eliminate x, let's subtract the first equation from the second equation:

(x + 5y) - (x - 2y) = -12 - 9
x + 5y - x + 2y = -21
7y = -21
y = -3

Now that we have found the value of y, we can substitute it back into the first equation to find x:

x - 2(-3) = 9
x + 6 = 9
x = 3

So the solution to the system of equations is x = 3, y = -3.

Now, let's find the intercepts:

To find the x-intercept, set y = 0 in the first equation:
x - 2(0) = 9
x = 9
x-intercept: (9, 0)

To find the y-intercept, set x = 0 in the first equation:
0 - 2y = 9
-2y = 9
y = -4.5
y-intercept: (0, -4.5)

Therefore, the correct solution to the system of equations is x = 3, y = -3, and the x-intercept is (9, 0) while the y-intercept is (0, -4.5). Thank you for your patience.