Final answer:
The system of equations is solved using the elimination method. By manipulating the equations to eliminate one variable, we found that x = -2 and y = -6.
Step-by-step explanation:
To solve the given system of equations by elimination method, we have:
- -7x + 5y = -16 (Equation 1)
- -10x + 2y = 8 (Equation 2)
First, we need to manipulate the equations so that one variable can be eliminated when we add or subtract the equations from each other. Let's eliminate the variable x. To do this, we look for the Least Common Multiple (LCM) of the coefficients of x, which are 7 and 10. The LCM is 70, so we will multiply Equation 1 by 10 and Equation 2 by 7:
- 10(-7x + 5y) = 10(-16)
- 7(-10x + 2y) = 7(8)
Which gives us:
- -70x + 50y = -160 (Equation 3)
- -70x + 14y = 56 (Equation 4)
Next, we subtract Equation 4 from Equation 3 to eliminate x:
-70x + 50y - (-70x + 14y) = -160 - 56
Simplifying that gives us:
36y = -216
Dividing both sides by 36, we get:
y = -6
Now, substitute the value of y back into one of the original equations to find the value of x. Let's use Equation 1 for that:
-7x + 5(-6) = -16
-7x - 30 = -16
-7x = 14
x = -2
Therefore, the solution to the system of equations is x = -2 and y = -6.
To check if this solution is reasonable and correct, we can substitute these values back into the original equations to see if they hold true.