Unit 5: Systems of Linear Equations · NY-8.EE.8, AI-A.REI.6, AI-A.REI.11
Both exams
Notes
Three geometric stories. One intersection: one solution. Parallel distinct lines: no solution. Same line: infinitely many solutions.
Substitution. Solve one equation for a variable, substitute into the other, then back-substitute. Best when a variable already has coefficient 1.
Elimination. Multiply so coefficients of one variable are opposites, add the equations, solve, then find the other variable.
Vocabulary
system of equations: Two or more equations considered together.
solution of a system: An ordered pair that satisfies every equation in the system.
Practice (no calculator unless marked)
Courtney spent $15.50 on four lattes and two donuts. The next day she spent $18.10 on three lattes and five donuts. If x is the cost of one latte and y is the cost of one donut, which system models this situation?
A. 4x + 2y = 18.10 and 3x + 5y = 15.50
B. x + y = 15.50 and x + y = 18.10
C. 4x + 2y = 15.50 and 3x + 5y = 18.10
D. 4x + 5y = 15.50 and 3x + 2y = 18.10
Dana went shopping for plants. She bought three roses and two daisies for $31.88. Later that day she bought two roses and one daisy for $18.92. If r is the cost of one rose and d is the cost of one daisy, which system models this situation?
A. 3r + 2d = 31.88 and 2r + d = 18.92
B. 3r + 2d = 18.92 and 2r + d = 31.88
C. r + d = 31.88 and r + d = 18.92
D. 3r + 2d = 31.88 and 2r + 2d = 18.92
The system y = x² − 3x − 6 and y = x − 1 is graphed. State the coordinates of the solution with the larger x-value as an ordered pair.
Courtney spent $15.50 on four lattes and two donuts. The next day she spent $18.10 on three lattes and five donuts. If x is the cost of one latte and y is the cost of one donut, which system models this situation?
A. 4x + 2y = 18.10 and 3x + 5y = 15.50
B. x + y = 15.50 and x + y = 18.10
C. 4x + 2y = 15.50 and 3x + 5y = 18.10
D. 4x + 5y = 15.50 and 3x + 2y = 18.10
Dana went shopping for plants. She bought three roses and two daisies for $31.88. Later that day she bought two roses and one daisy for $18.92. If r is the cost of one rose and d is the cost of one daisy, which system models this situation?
A. 3r + 2d = 31.88 and 2r + d = 18.92
B. 3r + 2d = 18.92 and 2r + d = 31.88
C. r + d = 31.88 and r + d = 18.92
D. 3r + 2d = 31.88 and 2r + 2d = 18.92
The system y = x² − 3x − 6 and y = x − 1 is graphed. State the coordinates of the solution with the larger x-value as an ordered pair.
Courtney spent $15.50 on four lattes and two donuts. The next day she spent $18.10 on three lattes and five donuts. If x is the cost of one latte and y is the cost of one donut, which system models this situation?
A. 4x + 2y = 18.10 and 3x + 5y = 15.50
B. x + y = 15.50 and x + y = 18.10
C. 4x + 2y = 15.50 and 3x + 5y = 18.10
D. 4x + 5y = 15.50 and 3x + 2y = 18.10
Dana went shopping for plants. She bought three roses and two daisies for $31.88. Later that day she bought two roses and one daisy for $18.92. If r is the cost of one rose and d is the cost of one daisy, which system models this situation?