System of Equations — Quiz 5

Questions in this quiz (6)

1. What is the value of the sum of $$x$$ and $$y$$ at the point of intersection for the two lines with the equations:$$\frac{2}{3}x+\frac{1}{4}y=5$$$$\frac{5}{6}x-\frac{1}{2}y=1$$

   • $$\frac{163}{8}$$
   • $$66$$
   • $$60$$
   • $$\frac{150}{13}$$

2. Solve the system of equations in two variables:(a) $$|x+2| + |x - y| = 0$$(b) $$(x + 2)^2 + y^2 = 0$$

   • $$(-2,-2)$$
   • $$(0,4)$$
   • $$(-2,0)$$
   • No real solution.

3. $$2x + y - 0.5z = 20$$$$3x - 2y + 1.5z = 30$$Find the value of $$x + y + z$$

   • 115
   • 70
   • 45
   • 120

4. Solve the pair of equations:$$\frac{1}{2x} + \frac{1}{3y} = 2$$$$\frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$$

   • $$(1,3)$$
   • $$(\frac{1}{3},\frac{1}{4})$$
   • $$(1,2)$$
   • $$(\frac{1}{2},\frac{1}{3})$$

5. The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Can you determine the length and breadth of the rectangle?

   • The length is $$17$$ units and the breadth is $$9$$ units.
   • The length is $$15$$ units and the breadth is $$10$$ units.
   • The length is $$22$$ units and the breadth is $$11$$ units.
   • The length is $$15$$ units and the breadth is $$12$$ units.

6. Solve the following system of equations:$$8v - 3u = 5uv$$ (1)$$6v - 5u = -2uv$$ (2)

   • $$u = \frac{1}{2}, v = \frac{1}{3}$$
   • $$u = \frac{1}{3}, v = \frac{1}{6}$$
   • $$u = \frac{2}{3}, v = \frac{31}{69}$$
   • $$u = \frac{2}{5}, v = \frac{11}{9}$$