Honors Algebra 2: Systems of 2 Linear Equations

Calculator Active, but only for arithmetic, unless otherwise specified.
  1. Solve using the graphing utility on your calculator. Answer to the nearest thousandth.\( \displaystyle \begin{align*} -\sqrt{2} \cdot x + \sqrt{3} \cdot y &= -4 \\ \pi x - 13y &= \sqrt{10} \end{align*} \)
    2. Solution (3.594, 0.625)
  2. Solve using substitution.\( \displaystyle \begin{align*} 6x - 5y &= 8 \\ x - 2y &= -1 \end{align*} \)
    3. Solution (3, 2)
  3. Solve by linear combinations.\( \displaystyle \begin{align*} \frac{x}{2} + \frac{y}{4} &= \frac{1}{4} \\ \frac{5x}{2} + y &= 2 \end{align*} \)
    4. Solution (2, -3)
  4. Solve by any method.\( \displaystyle \begin{align*} \frac{2x}{3} + \frac{3y}{5} &= 1 \\ x - \frac{3}{2} &= -\frac{9y}{10} \end{align*} \)
    5. Solution Dependent
  5. Solve by any method.\( \displaystyle \begin{align*} \frac{5x + 3y}{2} &= 2x - 3 \\ 5(y - x) &= 14y \end{align*} \)
    6. Solution (9, -5)
  6. Solve by any method.\( \displaystyle \begin{align*} 4x + 2y &= 6 \\ 3y &= -6x + 9 \end{align*} \)
    7. Solution Dependent
  7. Solve by any method. \( \displaystyle \begin{align*} 2(3x - 5y) &= 7 \\ 15y &= 9x + 1 \end{align*} \)
    8. Solution Inconsistent