1. Solve the system of equations by graphing:
$$y - \frac{1}{4}x = -1$$
$$y - 2 = 4x$$
2. Michael and Ashley each buy $x$ pounds of turkey and $y$ pounds of ham. Turkey costs 3 per pound at Store A and 4.5 per pound at Store B. Ham costs 4 per pound at Store A and 6 per pound at Store B. Michael spends 18 at Store A, and Ashley spends 27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham? Explain by solving the system:
$$3x + 4y = 18$$
$$4x + 6y = 27$$
3. Determine whether the system has one solution, no solution, or many solutions:
$$y - 13 = 5x$$
$$y - 5x = 12$$
4. Graph the system and find the solution(s):
$$y = \frac{1}{2}x + 1$$
$$-2x + 4y = 4$$
5. Use substitution to solve the system:
$$-3y = -2x - 1$$
$$y = x - 1$$
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These problems cover graphing linear equations, solving systems by substitution, and analyzing the number of solutions. Graph each pair of equations on coordinate axes to visualize the solutions.
Practice Systems 12C435
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