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Quiz 8
1. Use intercepts to graph $3x+5y=30$.
Solution: To find the $x$-intercept, set $y=0$ to get the equation $3x=30$ yielding the value $x=\dfrac{30}{3}=10$. Therefore the $x$-intercept is $(10,0)$. To find the $y$-intercept set $x=0$ to get the equation $5y=30$ yielding the value $y=\dfrac{30}{5}=6$. Therefore the $y$-intercept is $(0,6)$. Plot these points and connect the dots to complete the problem:

2. Solve by graphing: $\left\{ \begin{array}{ll} y=x+1 \\ y=-x-1 \\ \end{array} \right.$
Solution: The $y$-intercept of the first equation is $(0,1)$ and the $x$-intercept of the first equation is $(-1,0)$. The $y$-intercept of the second equation is $(0,-1)$ and the $x$-intercept is $(-1,0)$. Plot these and observe the intersection point to solve the system:

the intersection point is at $(-1,0)$, which is the solution.

3. Solve algebraically: $\left\{ \begin{array}{ll} y=x+1 & (i) \\ y=-x-1 & (ii) \\ \end{array} \right.$
Solution: Plug $y$ from equation (i) into equation (ii):
$$x+1=-x-1,$$ add $x$ to both sides to get $$2x+1=-1,$$ add $-1$ to both sides to get $$2x=-2,$$ now divide by $2$ to get $x=-1$. Take this value of $x$ and plug it into one of the two equations in the system, say (i), to get $y=(-1)+1=0$. Therefore the solution is $(-1,0)$.

4. Solve algebraically: $\left\{ \begin{array}{ll} 3x+6y=9 & (i) \\ 3x-y=9 & (ii). \end{array} \right.$
Solution: From equation (ii), solve for $y$ to get $$y=3x-9.$$ Plug this value of $y$ into (i) to get $$3x+6(3x-9)=9.$$ Expand the left hand side to get $$3x+18x-54=9.$$ Simplify the left and add $54$ to get $$21x=63.$$ Divide by $21$ to get $$x= \dfrac{63}{21} = 3.$$ Plug this value of $x$ into, say (i), to see that $$3(3)+6y=9.$$ Simplify the left to get $$9+6y=9.$$ Subtract $9$ to get $$6y=0,$$ and finally divide by $6$ to get $$y=0.$$ We have found the solution $(3,0)$.

5. Find an angle coterminal with $32^{\circ}$.
Solution: All angles coterminal with a given angle are found by adding or subtracting a multiple of $360^{\circ}$. So we could use, $$32^{\circ} + 360^{\circ} = 392^{\circ},$$ or many other possibilities.