For #43: k=9
Expand the right side of the equation by distributing the 3 to each term in the parentheses.
3(-1/4k +3)
3(-1/4k) + 3(3)
-3/4k + 9
So now we have:
1/4k = -3/4k + 9
Since both 1/4k and -3/4k are like terms with the same denominator, we can add -3/4k to both sides of the equation.
4/4k = 9
Since 4/4 is just equal to 1,
k = 9.
For #44: infinitely many solutions.
Distribute 13 to the term in the parentheses on the left side of the equation by multiplying.
13(y-3)
13(y) - 13(3)
13y -39
Notice how this is equal to the right side of the equation.
13y - 39 = 13y - 39
If you add 39 to both sides of the equation, then
13y = 13y
If you subtract 13y from the left side, then
0=0
If y = 0, then both sides of the equation are equal. It is true for all y. ALL values of y are solutions.
This is because if y = 1, then 13=13 which is true. No matter what value you put for y, the right and left sides of the equation will be equal. So ‘one solution’ and ‘no solution’ are incorrect. There are infinitely many solutions.