2.1.5 Practice

2.1.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

In questions 1 – 4, determine if the following points are solutions to the given system of equations.

1. Determine if the point is a solution to the system of equations: $\{\begin{array}{l}2x-<!--\; -\; -->6y=0\\ 3x-<!--\; -\; -->4y=5\end{array}$

1. $(1,\frac{3}{4})$
2. $(\frac{8}{7},\frac{6}{7})$
3. $(-<!--\; -\; -->3,4)$
4. $(3,1)$

2. Determine if the point is a solution to the system of equations: $\{\begin{array}{l}x-<!--\; -\; -->6y=0\\ 3x-<!--\; -\; -->4y=5\end{array}$

1. $(1,\frac{3}{4})$
2. $(\frac{8}{7},\frac{6}{7})$
3. $(-<!--\; -\; -->3,4)$
4. $(3,1)$

3. Determine if the point is a solution to the system of equations: $\{\begin{array}{l}x+y=2\\ y=\frac{3}{4}x\end{array}$

1. $(1,\frac{3}{4})$
2. $(\frac{8}{7},\frac{6}{7})$
3. $(-<!--\; -\; -->3,4)$
4. $(3,1)$

4. Determine if the point is a solution to the system of equations: $\{\begin{array}{l}4x+4y=7\\ y=\frac{3}{4}x\end{array}$

1. (1, $\frac{3}{4}$)
2. ($\frac{8}{7}$, $\frac{6}{7}$)
3. $(-<!--\; -\; -->3,4)$
4. $(3,1)$

5. Solve the system of equations by graphing: $\{\begin{array}{l}3x+y=-<!--\; -\; -->3\\ 2x+3y=5\end{array}$

1. $(4,-<!--\; -\; -->1)$
2. $(-<!--\; -\; -->3,6)$
3. $(0,-<!--\; -\; -->3)$
4. $(-<!--\; -\; -->2,3)$

Access multimedia content

6. Solve the system of equations by graphing: $\{\begin{array}{l}y=x+2\\ y=-<!--\; -\; -->2x+2\end{array}$

1. $(-<!--\; -\; -->2,0)$
2. $(0,2)$
3. $(-<!--\; -\; -->1,4)$
4. $(2,0)$

Access multimedia content

7. Solve the system of equations by graphing: $\{\begin{array}{l}y=\frac{3}{2}x+1\\ y=-<!--\; -\; -->\frac{1}{2}x+5\end{array}$

1. $(2,4)$
2. $(0,5)$
3. $(0,1)$
4. $(4,3)$

Access multimedia content

8. Solve the system of equations by graphing: $\{\begin{array}{l}x+y=-<!--\; -\; -->4\\ -<!--\; -\; -->x+2y=-<!--\; -\; -->2\end{array}$

1. $(-<!--\; -\; -->2,-<!--\; -\; -->2)$
2. $(4,1)$
3. $(-<!--\; -\; -->1,0)$
4. $(2,0)$

Access multimedia content

9. Solve the system of equations by graphing: $\{\begin{array}{l}-<!--\; -\; -->2x+3y=3\\ x+3y=12\end{array}$

1. $(0,1)$
2. $(3,3)$
3. $(4,0)$
4. $(6,2)$

Access multimedia content

10. Solve the system of equations by graphing: $\{\begin{array}{l}2x-<!--\; -\; -->4y=8\\ x+3y=9\end{array}$

1. $(8,2)$
2. $(-<!--\; -\; -->2,0)$
3. $(4,0)$
4. $(6,1)$

Access multimedia content

11. A bakery charges $2 per croissant and $4 per muffin. One day, they charge $42 in total and sell 15 baked goods. How many croissants and muffins did they sell?

1. 8 croissants and 7 muffins
2. 10 croissants and 5 muffins
3. 9 croissants and 6 muffins
4. 5 croissants and 10 muffins

12. A pet store sells mice for $7 each and gerbils for $9 each. They sell 17 animals for a total of $137. How many mice and gerbils did they sell?

1. 6 mice and 11 gerbils
2. 7 mice and 10 gerbils
3. 8 mice and 9 gerbils
4. 15 mice and 2 gerbils