If \(\frac{10(x^{2}y)}{xy^{2}}\) = 5y, what is the value of y in terms of x?
-
Solution
Isolate y on one side of the equation;\(\frac{10(x^{2}y)}{(xy^{2})}\) = 5y,10(x⁄y) = 5y, 10x = 5y2, 2x = y2, y = \(\sqrt{2x}\).
If 8x2 – 4y2 + x2 = 0, what is the value of x in terms of y?
-
Solution
Isolate x on one side of the equation; 8x2 – 4y2 + x2 = 0, 9x2 – 4y2 = 0, 9x2 = 4y2, x2 = (4⁄9)y2, x = (2⁄3)y.
If 4g2 – 1 = 16h2 – 1, what is the value of g in terms of h?
-
Solution
Isolate g on one side of the equation; 4g2 – 1= 16h2 – 1, 4g2 = 16h2, g2 = 4h2, g = 2h.
If a(3a) – b(4 + a) = –(a2 + ab), what is the value of b in terms of a?
-
Solution
Isolate b on one side of the equation; a(3a) – b(4 + a) = –(a2 + ab), 3a2 – 4b – ab = –a2 – ab, 4a2 – 4b = 0, 4a2 = 4b, b = a2.
If fg + 2f – g = 2 – (f + g), what is the value of g in terms of f ?
-
Solution
Isolate g on one side of the equation; fg + 2f – g = 2 – (f + g), fg + 2f – g = 2 – f – g, fg = 2 – 3f, g =\(\frac{2-3f}{f}\).
If 4(x⁄y + 1) = 10, what is the value of y in terms of x?
-
Solution
Isolate y on one side of the equation. Multiply the (x⁄y + 1) term by 4. Then, multiply both sides of the equation by y to make it easier to work
with; 4(x⁄y + 1) = 10,\(\frac{4x}{y}\) + 4 = 10, 4x + 4y = 10y, 4x = 6y, y = (2⁄3)x.
If 7a + 20b = 28 – b, what is the value of a in terms of b?
-
Solution
Isolate a on one side of the equation. Subtract 20b from both sides of the equation and divide by 7: 7a + 20b = 28 – b, 7a = 28 – 21b, a = 4 – 3b.
If (3⁄2)g = 9h – 15, what is the value of g in terms of h?
-
Solution
Isolate g on one side of the equation. Multiply both sides of the equation by 2⁄3: (2⁄3)(\(\frac{3}{2g}\)) = (9h – 15)2⁄3, g = 6h – 10.
When a = 1 and b = –1, ab + a⁄b+ a2 – b2 =
-
Solution
Substitute 1 for each instance of a and substitute –1 for each instance of b in the expression: (1)(–1) + \(\frac{1}{-1}\) + (1)2 – (–1)2 = –1 + (–1) + 1 – 1 = –2.
When x = 2 and y = 3,\(\frac{6x^{2}}{2y^{2}}+\frac{4x}{3y}\) =
-
Solution
Substitute 2 for each instance of x and substitute 3 for each instance of y in the expression:\(\frac{6(2)^{2}}{2(3)^{2}}+\frac{4(2)}{3(3)}=\frac{(6)(4)}{(2)(9)}+\frac{8}{9}=\frac{24}{18}+\frac{8}{9}=\frac{12}{9}+\frac{8}{9}=\frac{20}{9}\)