System of Equations — Quiz 4

Questions in this quiz (6)

1. Consider the system of equations:$$3x + 4y = 12$$$$9x + 12y = 36$$For each real number $$r$$, which of the following points lies on the graph of each equation in the $$xy$$-plane for the given system?

   • $$(\frac{r}{4} + 3, -\frac{r}{4} + 9)$$
   • $$(-\frac{2r}{3} + 4, r)$$
   • $$(r, -\frac{2r}{3} + 4)$$
   • $$(r, \frac{3r}{4} + 6)$$

2. If $$5^c = 25$$ and $$125^{c+d} = 625$$, what is $$d$$?

   • $$\frac{4}{3}$$
   • $$-\frac{3}{2}$$
   • $$\frac{3}{2}$$
   • $$-\frac{2}{3}$$

3. If $$(\sqrt{3})^x = 27^y$$ and $$9^x \cdot 3^y = 729$$, what is $$x$$?

   • $$\frac{6}{13}$$
   • $$\frac{36}{13}$$
   • $$\frac{3}{13}$$
   • $$\frac{16}{13}$$

4. When the City Transportation Department in Mapleton decreases the cost of 1-day local transit passes, the number of passes sold per hour increases. The expression $$rx+s$$ represents the number of passes sold per hour when the price is $$x$$ dollars per pass. When the price was $$3$$, the number of passes sold per hour was $$60$$. When the price decreased to $$1$$, the number of passes sold per hour increased to $$100$$. What are the values of $$r$$ and $$s$$?

   • $$r=-20, s=120$$
   • $$r=-30, s=150$$
   • $$r=-25, s=135$$
   • $$r=-40, s=180$$

5. Solve for $$y$$ in the following system of linear equations:$$2x+3y+5z=12$$$$y-2z=4$$$$x+y=6$$

   • $$7$$
   • $$\frac{7}{12}$$
   • $$\frac{20}{7}$$
   • $$\frac{10}{3}$$

6. In the system of equations shown below, what value of $$k$$ will create a system of equations that has no solutions?$$8x+5y=20$$$$12x+ky=30$$

   • $$12$$
   • $$10$$
   • $$7$$
   • $$7.5$$