Answer:
1. Step 3
2. Multiply the first equation by -2, the second by 3. (1, 1)
Step-by-step explanation:
1. "Combine like terms" means combine terms with the same constellation of variables to the same degree. In this linear equation, combining like terms would be (a) combining x-terms; and/or (b) combining constants.
In the solution process, there are no x-terms that are combined anywhere, but in step 3 we have performed the additions 6-6 = 0 and 41-6 = 35, combining the constants on either side of the equal sign. That is, Step 3 is the result of combining like terms (constants).
__
2. To eliminate a variable you need to have its coefficient in the combined equations by zero. That can be accomplished by multiplying the first equation by the opposite of the variable's coefficient in the second equation, and multiplying the second equation by the variable's coefficient in the first equation.
Here, the x-coefficients are 3 and 2, so multiplying the first equation by -2 and the second by 3 will result in x-coefficients of -6 and 6, which will have a sum of zero.
Doing that, we get ...
-2(3x -5y) +3(2x +y) = -2(-2) +3(3)
10y +3y = 4 + 9 . . . . . eliminate parentheses
13y = 13 . . . . . . . . . . . combine like terms
y = 1 . . . . . . . . . . . . . . . divide by 13
Substituting this value into the second equation gives ...
2x +1 = 3
2x = 2 . . . . . . . . subtract 1
x = 1 . . . . . . . . . . divide by 2
The solution is (x, y) = (1, 1).
