Answer:
Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.
Explanation:
The given equation is:
-x + 3y = 11
To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.
Let's suppose we have another equation with x, for example:
2x + 5y = 7
We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:
-2x + 6y = 22 (multiply the first equation by -2)
2x + 5y = 7 (the second equation)
Now we can add the two equations to eliminate x:
-2x + 2x + 6y + 5y = 22 + 7
Simplifying the equation, we get:
11y = 29
Dividing both sides by 11, we get:
y = 29/11
Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
-x + 3y = 11
Substituting y = 29/11, we get:
-x + 3(29/11) = 11
Simplifying the equation, we get:
-x + 87/11 = 11
Subtracting 87/11 from both sides, we get:
-x = 11 - 87/11
Multiplying both sides by -1, we get:
x = 87/11 - 11
Simplifying the equation, we get:
x = (87 - 121)/11
x = -34/11