Solve the system using elimination. Express as ordered pair.
2x - 7y = 27
3x = 2y = 3
The question as is would provide 3 equations for two unknowns.
It would be a good idea to check the question before/after posting.
My math teacher gave it to me on a worksheet, this is the only one I don't understand.
To solve the system of equations using elimination, we need to eliminate one of the variables by manipulating the equations.
Let's start by multiplying both sides of the second equation by 2 to simplify it:
3x - 2y = 6
Now we have the system:
2x - 7y = 27
3x - 2y = 6
To eliminate the y-variable, we can multiply the first equation by 2 and the second equation by 7:
(2)(2x - 7y) = (2)(27)
(7)(3x - 2y) = (7)(6)
This simplifies to:
4x - 14y = 54
21x - 14y = 42
Now, subtract the second equation from the first:
(4x - 14y) - (21x - 14y) = 54 - 42
This gives us:
-17x = 12
To solve for x, divide both sides by -17:
x = -12/17
Now substitute this value back into one of the original equations, let's choose the first equation:
2(-12/17) - 7y = 27
Simplify:
-24/17 - 7y = 27
To solve for y, subtract -24/17 from both sides and then divide by -7:
-7y = 27 + 24/17
-7y = (459 + 24)/17
-7y = 483/17
Divide both sides by -7:
y = (483/17) / -7
y = -69/17
Therefore, the solution to the system of equations is (x, y) = (-12/17, -69/17).