which ordered pair is the solution for the system?
2x - 3y = -19
4x + 5y = 17
To find the solution for the given system of equations:
Equation 1: 2x - 3y = -19
Equation 2: 4x + 5y = 17
We can solve this system by using the method of substitution or elimination. Here, we'll use the method of elimination.
To eliminate the y variable, we can multiply Equation 1 by 5 and Equation 2 by 3. This will allow us to cancel out the y terms when adding the two equations together.
Multiplying Equation 1 by 5:
5(2x - 3y) = 5(-19)
10x - 15y = -95
Multiplying Equation 2 by 3:
3(4x + 5y) = 3(17)
12x + 15y = 51
Now, let's add these two equations:
(10x - 15y) + (12x + 15y) = -95 + 51
10x - 15y + 12x + 15y = -44
22x = -44
Dividing both sides of the equation by 22:
x = -44/22
x = -2
Now, substitute the value of x back into any one of the equations. Let's use Equation 1:
2x - 3y = -19
2(-2) - 3y = -19
-4 - 3y = -19
-3y = -19 + 4
-3y = -15
Dividing both sides of the equation by -3:
y = -15/-3
y = 5
Therefore, the ordered pair (-2, 5) is the solution for the given system of equations.