To solve the system of equations using elimination, we want to eliminate one variable by multiplying both equations by appropriate values so that the coefficients of that variable will cancel out when we add the two equations together.
Let's start by multiplying the first equation by 2 and the second equation by 7 to eliminate the x variable.
2(7x-6y) = 2(-2) becomes 14x-12y = -4
7(2x-7y) = 7(10) becomes 14x-49y = 70
Now, we can add the two equations together:
(14x-12y) + (14x-49y) = -4 + 70
Combining like terms:
28x - 61y = 66
Now we have a new equation with only one variable. Let's solve for x or y.
To eliminate the x variable, we can multiply the first equation by 14 and the second equation by 7:
14(7x-6y) = 14(-2) becomes 98x-84y = -28
7(2x-7y) = 7(10) becomes 14x-49y = 70
Adding the two equations together:
(98x-84y) + (14x-49y) = -28 + 70
Combining like terms:
112x - 133y = 42
Now we have another new equation with only one variable. Let's solve for x or y.
By using the elimination method, we obtained two different equations: 28x - 61y = 66 and 112x - 133y = 42.
At this point, we have two options:
1. Solve the first equation for x or y, substitute the result into the second equation, and solve for the remaining variable.
2. Solve the second equation for x or y, substitute the result into the first equation, and solve for the remaining variable.
Either method will give us the values of x and y that satisfy both equations