Homework

Problem 1 · easy

Solve by substitution: { y = 3x - 1; 2x + y = 9 }

Problem 2 · easy

Solve by substitution: { x = 2y + 3; 3x - y = 14 }

Problem 3 · easy

Solve by elimination: { x + y = 10; x - y = 4 }

Problem 4 · medium

Solve by elimination: { 2x + 3y = 13; 2x - y = 5 }

Problem 5 · medium

Solve by elimination: { 3x + 2y = 11; x - 4y = 5 }

Problem 6 · easy

Identify: { 2x + y = 5; 4x + 2y = 10 }. How many solutions?

Problem 7 · medium

Identify: { x - 3y = 4; -2x + 6y = 3 }. How many solutions?

Problem 8 · medium

A store sells adult tickets for $8 and children's tickets for $5. A total of 200 tickets were sold for $1,270. How many adult tickets were sold?

Problem 9 · medium

Solve: { 4x - y = 3; 3x + 2y = 14 }

Problem 10 · medium

A coffee blend uses beans at $4/lb and $6/lb. A 20-lb blend costs $96. How many pounds of each?

Problem 11 · medium

Solve: { x/2 + y/3 = 4; x - y = 6 }

Problem 12 · medium

Solve: { 5x + 3y = 15; 10x + 6y = 25 }. How many solutions?

Problem 13 · medium

A boat travels 48 miles downstream in 3 hours and 48 miles upstream in 6 hours. Find the speed of the current.

Problem 14 · medium

$8000 is invested at 3% and 5%. Total annual interest is $320. How much is at 3%?

Problem 15 · challenge

How many mL of 10% salt solution and 25% salt solution must be mixed to make 200 mL of 20% salt solution?

Problem 16 · medium

Solve by substitution: { 3x - y = -1; x + 4y = 14 }

Problem 17 · easy

Solve: { y = (1/2)x + 1; y = -x + 4 }

Problem 18 · easy

A rope 48 m long is cut into two pieces. One piece is 8 m longer than the other. Find the lengths.

Problem 19 · challenge

Solve: { 2x + 5y = 1; -4x + 3y = -35 }

Problem 20 · challenge

Solve: { 0.2x + 0.3y = 1.3; 0.4x - 0.1y = 0.9 }

Problem 21 · easy

Two angles are supplementary (sum to 180). One is 40 more than the other. Find both angles.

Problem 22 · medium

Solve by elimination: { 6x - 4y = 2; -9x + 6y = -3 }

Problem 23 · easy

Find two numbers whose sum is 80 and difference is 12.

Problem 24 · challenge

Solve: { 3x + 4y - z = 7; x + 2y + z = 5; 2x - y + 3z = 8 } — find z only.

Problem 25 · medium

A mix of 40 coins (nickels and dimes) is worth $3.25. How many dimes are there?