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What is the correct solution for the system of equations $egin{cases} y = 2x + 5 \ y = -x \ ext{?} \ ext{A: (1, 7)} \ ext{B: (2, 9)} \ ext{C: (3, 11)} \ ext{D: (4, 13)} \ ext{E: (5, 15)} \ ext{F: (6, 17)} \ ext{G: (0, 5)} $
What is the correct solution for the system of equations $egin{cases} y = 2x + 5 \ y = -x \ ext{?} \ ext{A: (1, 7)} \ ext{B: (2, 9)} \ ext{C: (3, 11)} \ ext{D: (4, 13)} \ ext{E: (5, 15)} \ ext{F: (6, 17)} \ ext{G: (0, 5)} $
The equations $y = -4x + 2$ and $y = -4x - 5$ have no solution.
The equations $y = -4x + 2$ and $y = -4x - 5$ have no solution.
True
Write the system of equations that represents Richard and Teo's ages, given Richard is 8 years older than twice Teo's age and their combined age is 29.
Write the system of equations that represents Richard and Teo's ages, given Richard is 8 years older than twice Teo's age and their combined age is 29.
x + y = 29 and x = 2y + 8
Skyler buys 22 T-Shirts and 51 hats for $800. The next day, he buys 8 T-Shirts and 3 hats for $110. Write the system of equations: $22T + 51H = 800$ and $8T + 3H = ______
Skyler buys 22 T-Shirts and 51 hats for $800. The next day, he buys 8 T-Shirts and 3 hats for $110. Write the system of equations: $22T + 51H = 800$ and $8T + 3H = ______
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Match the following systems of equations to their classification (no solution, one solution, infinitely many solutions):
Match the following systems of equations to their classification (no solution, one solution, infinitely many solutions):
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Which system of equations would indicate one unique solution? (Select one)
Which system of equations would indicate one unique solution? (Select one)
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The ordered pair (9, 10) is a solution for the inequality $y > 5x + 2$.
The ordered pair (9, 10) is a solution for the inequality $y > 5x + 2$.
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What is the combined age of Richard and Teo if Richard's age is represented by the equation $x = 2y + 8$?
What is the combined age of Richard and Teo if Richard's age is represented by the equation $x = 2y + 8$?
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In the system $egin{cases} y = 2x + 5 \ y = -x \ ext{the intersection point is at } (x, y) = ______
In the system $egin{cases} y = 2x + 5 \ y = -x \ ext{the intersection point is at } (x, y) = ______
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Study Notes
8th Grade Math - 1st Term Revision Sheet
- Revision sheet for 8th Grade Math, 1st Term Exam
- Topics covered include solving systems of equations by graphing and substitution, solving word problems using systems of equations, and inequalities.
Systems of Equations (Graphing)
- Question 1: Find the solution for the system of equations: y = 2x + 5 and y = 1/2x
- Question 2: Find the solution for the system of equations: y = -4x + 2 and y = -4x + 5
- Question 3: Find the solution for the system of equations: 15x + 5y = 25 and y = -3x + 5
- Question 4 (a): Determine if the system of equations shown in the graph has no solution, infinitely many solutions, or one solution.
Systems of Equations (Substitution)
- Question 1 (QB): Solve the system using substitution: y = x - 1 and x + y = 7
- Question 2 (QB): Solve the system using substitution: 4x + 8y = -8 and x = -2y + 1
- Question 3 (QB): Solve the system using substitution: y = 2x + 1 and 4y – 5x = 13
- Question 4 (QD): Solve the system using substitution: x - y = 4 and 2x + y = 5
- Question 5 (QD): Solve the system using substitution: 3x + 2y = 8 and x + 4y = −4
- Question 6 (QD): Solve the system using substitution: 4x - 3y = 17 and 2x – 5y = 5
- Question 7 (QD): Solve the system using substitution: 7x - 4y = -12 and x-2y = 4
Word Problems using Systems of Equations (Qc)
- Question 1: Richard and Teo have a combined age of 29. Richard is 8 years older than twice Teo's age. Write a system of equations to represent the situation.
- Question 2: Skyler buys 22 T-shirts and 51 hats for $800. The next day, he buys 8 T-shirts and 3 hats for $110. Write a system of equations that can be used to solve the problem.
- Question 3: A vacation resort offers surfing lessons and parasailing. If a person takes a surfing lesson and goes parasailing, she will pay a total of $175. On Friday the resort collected a total of $3,101 for activities. Write a system of equations that can be used to solve the problem.
- Question 4: 4x + 3y = 30 and x = 5y - 4
- Question 5: 2x + 2y = 6 and 4x + 4y = 4
Equivalence of Systems of Equations (QE)
- Question 1: Are the systems of equations equivalent: 3x - 9y = 5, 6x + 2y = 18 and 6x – 9y = 10, 6x + 2y = 18
- Question 2: Are the systems of equations equivalent: 4y + 2x = -7 and 2y – 6x = 8, 4y + 2x = -7 and 4y - 12x = 16
Inequalities (QF and QG and QH)
- Question 1 (QF): Determine the inequality represented in the graph.
- Question 2 (QF): Determine the system of inequalities represented in the graph.
- Question 3: Determine the inequality shown by the ordered pairs (5, -2) and (9, 10).
- Question 4 (QH): Determine the system of inequalities represented in the graph.
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Description
Prepare for your 1st term math exam with this comprehensive revision sheet covering systems of equations. Topics include graphing techniques, substitution methods, and word problems involving inequalities. Test your understanding and boost your confidence before the exam!
