Homework

Problem 1 · easy

Solve by substitution: x + y = 10 and y = 2x + 1.

Problem 2 · easy

Solve by substitution: 3x - y = 5 and y = x - 1.

Problem 3 · easy

Solve by elimination: x + y = 8 and x - y = 2.

Problem 4 · medium

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

Problem 5 · easy

Identify: is the system x + y = 4 and 2x + 2y = 9 consistent or inconsistent?

Problem 6 · easy

Identify: is the system 3x - y = 5 and 6x - 2y = 10 independent or dependent?

Problem 7 · easy

Write the augmented matrix for: 2x + y = 7 and 3x - 2y = 1.

Problem 8 · medium

Solve using matrices: x + 2y = 5 and 2x - y = 0.

Problem 9 · medium

A mix of $3 and $5 items totaling 20 items costs $76. How many of each?

Problem 10 · easy

Two numbers sum to 50 and their difference is 18. Find them.

Problem 11 · medium

A plane travels 600 miles with the wind in 2 hours and 600 miles against it in 3 hours. Find the plane speed and wind speed.

Problem 12 · easy

Solve the nonlinear system: y = x^2 and y = 4.

Problem 13 · medium

Solve: y = x^2 - 1 and y = 2x + 2.

Problem 14 · medium

Solve: x^2 + y^2 = 10 and x + y = 4.

Problem 15 · medium

Solve the 3x3 system using back-substitution: z=2, y+z=5, x+y+z=9.

Problem 16 · medium

Set up (do not solve) a 3x3 system for: John is twice as old as Mary, their ages sum to 45, and John is 5 older than twice Sam's age.

Problem 17 · medium

How many solutions does the system x^2 + y^2 = 4 and x^2 + y^2 = 9 have?

Problem 18 · challenge

Solve: x - y = 3 and x*y = 4.

Problem 19 · medium

A fruit stand mixes apples ($1.20 each) and oranges ($0.80 each). 30 pieces total cost $30. How many of each?

Problem 20 · medium

Perform one row operation on this matrix: R2 = R2 - 2*R1 for [[1,3,5],[2,1,4]].

Problem 21 · challenge

Solve: y = e^x and y = e^(-x) + 1. How many intersections does this system have?

Problem 22 · challenge

Solve by elimination: 5x - 3y = 11 and 3x + 2y = 7.

Problem 23 · medium

Solve: x + y = 0 and x^2 - y = 2.

Problem 24 · medium

Find where y = x + 1 and y = x^2 - 1 intersect.

Problem 25 · easy

A 3x3 system gives the augmented matrix [[1,0,0,3],[0,1,0,-1],[0,0,1,5]]. Write the solution.