Answer:
Explanation:
To solve the system of equations:
Equation 1: 6x + 5y = 1
Equation 2: 7x + 8y = -14
We can use the method of substitution or elimination. Let's solve it using the elimination method.
First, we need to manipulate the equations to obtain the same coefficient for one of the variables.
Let's multiply Equation 1 by 7 to make the coefficient of x the same as the coefficient of x in Equation 2:
Equation 1 (new): 42x + 35y = 7
Equation 2: 7x + 8y = -14
Now, we'll subtract Equation 2 from Equation 1:
(42x + 35y) - (7x + 8y) = 7 - (-14)
Simplifying, we have:
35x + 27y = 21
Now we have a new equation:
Equation 3: 35x + 27y = 21
We'll solve Equations 2 and 3 as a system of linear equations:
Equation 2: 7x + 8y = -14
Equation 3: 35x + 27y = 21
Let's multiply Equation 2 by 5 and Equation 3 by 7 to make the coefficient of y the same:
Equation 2 (new): 35x + 40y = -70
Equation 3 (new): 35x + 27y = 21
Now, we'll subtract Equation 2 from Equation 3:
(35x + 27y) - (35x + 40y) = 21 - (-70)
Simplifying, we have:
-13y = 91
Dividing both sides by -13, we get:
y = -7
Now we'll substitute the value of y (-7) into Equation 2 to solve for x:
7x + 8(-7) = -14
Simplifying, we have:
7x - 56 = -14
Adding 56 to both sides, we get:
7x = 42
Dividing both sides by 7, we get:
x = 6
Therefore, the solution to the system of equations is:
x = 6
y = -7