Algebra Chapter: Solving Systems Flashcards

Solve the system: 4x + 2y = 7, y = 5x.

Solve the system: X + 3y = 7, 2x - 4y = 24.

Solve the system: r + s = -12, 4r - 6s = 12.

Solve the system: x + y = 12, x - y = 2.

Solve the system: 4x - 6y = -26, -2x + 3y = 13.

Solve the system: 3a + 4b = 9, -3a - 2b = -3.

Solve the system: 7x + 2y = -8, 8y = 4x.

A student has some $1 bills and $5 bills in his wallet. He has a total of 15 bills that are worth $47. How many of each type of bill does he have?

Jenny's bakery sells carrot muffins for $2.00 each. The electricity to run the oven is $120.00 per day and the cost of making one carrot muffin is $1.40. How many muffins need to be sold each day for the bakery to break even?

Determine which equations below, when combined with the equation 3x - 4y = 2, will form a system with no solutions. Choose all that apply.

Solving Systems Algebraically

To solve linear systems, find the intersection point of equations representing lines.
Methodologies include substitution, elimination, or graphical representation.

Specific Solutions

4x + 2y = 7, y = 5x results in the solution (0.5, 2.5).
x + 3y = 7, 2x - 4y = 24 leads to the solution (10, -1).
r + s = -12, 4r - 6s = 12 gives the solution (-6, -6).
x + y = 12, x - y = 2 produces the solution (7, 5).
4x - 6y = -26, -2x + 3y = 13 results in an infinite number of solutions.

Additional Problems

3a + 4b = 9, -3a - 2b = -3 leads to the solution (-1, 3).
7x + 2y = -8, 8y = 4x provides the solution (-1, -0.5).

Real-Life Application: Linear Word Problems

A student with $1 and $5 bills has 7 $1 bills and 8 $5 bills, totaling 15 bills worth $47.
To break even, 200 carrot muffins need to be sold daily, with sales priced at $2.00 each against $1.40 cost of production plus $120 daily overhead.