Unit 6 test: Systems of Equations and Inequalities

Is $(-1, 4)$ a solution of the system $y = -2x + 2$ and $x + y = 3$?

Solve by graphing: $y = x - 3$ and $y = -2x + 3$.

How many solutions does the system $3x - y = 4$ and $y = 3x + 2$ have?

Solve by substitution: $y = 4x - 1$ and $3x + 2y = 20$.

Solve by substitution: $x - 5y = 3$ and $2x + 3y = 19$.

Solve by elimination: $4x + y = 9$ and $2x - y = 3$.

Solve by elimination: $3x + 5y = -1$ and $2x - 3y = 12$.

In the solution of the system $5x - 2y = 1$ and $3x + 4y = 37$, what is the value of $y$?

What is the solution of the system $2x + 6y = 8$ and $x + 3y = 4$?

A farm has $40$ animals, all chickens and goats. Together they have $110$ legs. How many goats are there?

How many liters of a $20\%$ salt solution must be mixed with a $50\%$ salt solution to make $30$ liters of a $40\%$ salt solution?

A kayaker paddles $12$ miles downstream in $2$ hours and $12$ miles back upstream in $3$ hours. What is the kayaker's speed in still water, in miles per hour?

Which point is a solution of the system $y \ge -x + 1$ and $y < 2x - 1$?

Which graph description matches the system $y > \dfrac{1}{2}x + 1$ and $y \le -x + 4$?

Jordan earns $10 per hour mowing lawns and $15 per hour tutoring. Jordan can work at most $12$ hours a week and wants to earn at least $150. If Jordan tutors for $6$ hours, what is the least number of hours of mowing that meets both conditions?