Solve the system of equations.
6x–5y=27
3x+5y=36
To solve the system of equations, we can either use substitution or elimination method.
Using the elimination method, we can add both equations together to eliminate the "y" term:
(6x - 5y) + (3x + 5y) = 27 + 36
9x = 63
Dividing both sides of the equation by 9 gives:
x = 7
Substituting the value of x into one of the original equations to solve for y, we have:
6(7) - 5y = 27
42 - 5y = 27
Subtracting 42 from both sides of the equation gives:
-5y = -15
Dividing both sides of the equation by -5 gives:
y = 3
Thus, the solution to the system of equations is x = 7 and y = 3.
To solve the system of equations, we can use the method of elimination. Adding the equations together will eliminate the variable "y":
(6x - 5y) + (3x + 5y) = 27 + 36
Combining like terms:
9x = 63
To solve for x, divide both sides by 9:
x = 63/9
Simplifying:
x = 7
Now, substitute the value of x back into either of the original equations to solve for y. We'll use the second equation:
3(7) + 5y = 36
Simplify:
21 + 5y = 36
Subtract 21 from both sides:
5y = 36 - 21
5y = 15
Next, divide both sides by 5 to solve for y:
y = 15/5
Simplify:
y = 3
Therefore, the solution to the system of equations is x = 7 and y = 3.
To solve the system of equations, we will use the method of elimination. The aim is to eliminate one variable so that we can solve for the other. In this case, we can eliminate the variable "y" by adding the two equations together.
Adding the equations will cancel out the "y" variable:
(6x - 5y) + (3x + 5y) = 27 + 36
Combining like terms:
9x = 63
Next, we can solve for "x" by dividing both sides of the equation by 9:
9x/9 = 63/9
Simplifying:
x = 7
Now that we have found the value of "x," we can substitute it back into one of the original equations to find the value of "y". Let's use the first equation:
6x - 5y = 27
Substituting x = 7:
6(7) - 5y = 27
Simplifying:
42 - 5y = 27
Next, we solve for "y" by isolating the variable:
-5y = 27 - 42
-5y = -15
Dividing both sides by -5:
-5y / -5 = -15 / -5
Simplifying:
y = 3
So, the solution to the system of equations is x = 7 and y = 3.