Solve one of the formulas for A, then substitute that into the other formula to solve for B, then substitute the solution for B into one of the formulas to solve for A. Here is how: Givens: A+B=8 A-B=9 So: If A+B=8 then A=8-B Next, substitute this into the other formula... A-B=9 (8-B)-B=9 (-B) - B = 1 (-2B) = 1 B= (- 1/2) Next, substitute the solution for B into one of the formulas to solve for A.... A+B=8 A+ (-1/2) = 8 A = 8 and 1/2 So... B= (- 1/2) A = 8 and 1/2
-1
B x A = BA
That factors to (a + 1)(a + b) a = -1, -b b = -a
b = 14
one a/b X b/a = a/a X b/b =1/1 = 1
0.6667
OK, so first let's translate it into math notation: 5/(2b)*2 = (b-1)/2 Now note that the 2 of 2b and the multiplication by 2 cancel out in the left side, giving 5/b = (b-1)/2 To get rid of the fractions, multiply both sides by 2b, giving: 5*2 = b*(b-1) simplify [b^2 = b*b is a notation for b squared] b^2 - b - 10 = 0 This is a second degree equation. Without using formulas to solve it, notice that each expression of the form b^2 + a*b = (b + a/2)^2 - (a^2)/4 this is called splitting off the square. In our case we get (b - 1/2)^2 - 1/4 - 10 = 0 or (b - 1/2)^2 = 1/4 + 10 hence (b - 1/2) = +- (41/4)^(1/2) = +- (1/2)*41^(1/2) 41^(1/2) is a notation for the square root of 41.
Solve one of the formulas for A, then substitute that into the other formula to solve for B, then substitute the solution for B into one of the formulas to solve for A. Here is how: Givens: A+B=8 A-B=9 So: If A+B=8 then A=8-B Next, substitute this into the other formula... A-B=9 (8-B)-B=9 (-B) - B = 1 (-2B) = 1 B= (- 1/2) Next, substitute the solution for B into one of the formulas to solve for A.... A+B=8 A+ (-1/2) = 8 A = 8 and 1/2 So... B= (- 1/2) A = 8 and 1/2
-1
B x A = BA
That factors to (a + 1)(a + b) a = -1, -b b = -a
-83
0.3333
b = 14
2 is
yes -a=-b means you multiplied each side by -1 which is allowed