A store sells pens and notebooks. Pens cost \$2 each and notebooks \$3 each. A customer buys some combination totaling \$29 for 11 items. Let p = pens, n = notebooks. If p = 11 - n, substitute and find the number of notebooks bought.

After substituting $y=2-x$ into $3x-4y=1$, simplify and solve for $x$.

Solve the system using substitution: { y = (3/4)x - 2 ; (1/2)x + (3/2)y = 6 }

When multiplying an entire equation by a scalar in the elimination process, what must you remember to do to every term?

Solve by elimination: $9x-6y=3$ and $3x+4y=11$. What is the final solution?

A student solved a system and reported the solution as $(x,y)=(-2,4)$. The original system was $\{\begin{array}{c}5x-2y=-18\\ -3x+y=10\end{array}$. Check the student's solution by substitution and decide whether it is correct.

Graph the inequality y ≥ -3x + 2. Using the test point (0,0), determine which side should be shaded.

Consider the system: y ≤ -x + 4 and y > (1/2)x - 1. Find the coordinates of the corner point where the two boundary lines intersect (the pair of boundary lines treated as equations).

A conference event has seating constraints. Room A can seat 3 per table and Room B can seat 5 per table. They must seat at least 100 total people and have at most 30 tables combined. Let a = the tables in Room A, and b = the tables in Room B. Form the system of inequalities and determine one feasible integer solution, $(a,b)$, that will meet both constraints. Show your work.