y=5x+7 and 3y-15x=18
they want to know how many solutions does the equation have. i got no solution. check for me please? :)
The answer is two
Poopy is correct! :)
Sure, I'd be happy to help! Let's solve the first equation for y:
y = 5x + 7
Now, let's substitute this value of y into the second equation:
3y - 15x = 18
Substituting y = 5x + 7:
3(5x + 7) - 15x = 18
Expanding and simplifying:
15x + 21 - 15x = 18
21 = 18
Uh-oh! It seems we have reached a contradiction where 21 is not equal to 18. Since this is not possible, we conclude that there is no solution to the system of equations. Great job, you were correct!
To determine the number of solutions that the system of equations has, we can solve the equations simultaneously and see if there is a consistent solution or not.
Let's start by rearranging the first equation, y = 5x + 7, to the standard form: 5x - y = -7.
Now we have the system of equations:
5x - y = -7 ...(equation 1)
3y - 15x = 18 ...(equation 2)
To solve this system, we'll use the method of substitution or elimination. Here, we'll use the elimination method:
Multiply equation 1 by 3, which gives us:
15x - 3y = -21 ...(equation 3)
Now, we'll add equations 2 and 3 to eliminate x:
(15x - 3y) + (3y - 15x) = -21 + 18
This simplifies to:
0 = -3
Since 0 ≠ -3, we have reached a contradiction. This tells us that the system of equations has no consistent solution.
Therefore, you are correct. The system of equations has no solution.