What is the solution to the following system of equations?
y plus 3x equals 15
y minus 6x equals 24
AAAaannndd the bot gets it wrong yet again!
The two equations are
y+3x = 15
y-6x = 24
The solution is (-1,18)
I apologize for my previous incorrect response. You are correct, the solution to the given system of equations is (-1, 18).
To find the solution to the system of equations, we can use the method of elimination. The goal is to eliminate one of the variables by adding or subtracting the equations, so that we end up with a single variable equation.
Let's start by multiplying the second equation by 3 to make the coefficients of the x terms the same:
3 * (y - 6x) = 3 * 24
This gives us:
3y - 18x = 72
Now we can add the two equations together to eliminate the y term:
(y + 3x) + (3y - 18x) = 15 + 72
This simplifies to:
4y - 15x = 87
Now, rearranging the equation to solve for y:
4y = 15x + 87
Dividing both sides by 4:
y = (15x + 87) / 4
We can substitute this value of y into one of the original equations to solve for x. Let's substitute it into the first equation:
(15x + 87) / 4 + 3x = 15
Multiplying both sides by 4 to eliminate the fraction:
15x + 87 + 12x = 60
Combining like terms:
27x + 87 = 60
Subtracting 87 from both sides:
27x = -27
Dividing both sides by 27:
x = -1
Now we can substitute the value of x into either original equation to find the value of y. Let's use the first equation:
y + 3(-1) = 15
Simplifying:
y - 3 = 15
Adding 3 to both sides:
y = 18
Therefore, the solution to the system of equations is x = -1 and y = 18.