Number Line
- x+y+z=25,\:5x+3y+2z=0,\:y-z=6
- x+2y=2x-5,\:x-y=3
- 5x+3y=7,\:3x-5y=-23
- x+z=1,\:x+2z=4
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- High School Math Solutions – Systems of Equations Calculator, Nonlinear In a previous post, we learned about how to solve a system of linear equations. In this post, we will learn how...
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- Mathematics
- High School
Lesson 3 Unit 7, Solving Systems Using Elimination Quiz 1. (I'VE ALREADY ANSWERED THIS) 2. What is the solution of the system? 7x + 5y = 19 -7x - 2y = -16 (A). (2, 1) (B). (1, 2) (C). (7, 5) (D). (-7, -2) 3. Which method would be the simplest way to slove the system? y = 1/2x 2x + 3y = 28 (A). Graphing (B). Substitution (C). Elimination (D). Distributive 4. What is the solution of the system? y = -3x 3x + 2y = 6 (A). (2, 6) (B). (-1, 3) (C). (-2, 6) (D). (1.5, -4.5) 5. How many solutions does this system have? -3x + 6y = 10 -3x + 6y = -4 (A). None (B). One (C). Infinite (D). Two 6. In wich quadrant does the solution of the system fall? y = x - 1 y = -3x - 5 (A). I (B). II (C). III (D). IV
Expert-verified answer.
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Step-by-step explanation:
2) Lets add 2 equation together, we will find:
If we put y value in the first equation:
3) Substation is the best way to solve the system.
Lets multiply first equation with 4:
Substitute 2x with 4y:
4) Again lets substitute 3x with -y:
Therefore x=-2
Correct answer is C
5) None of real numbers is the solution of this system.
6) First lets multiply first equation with -1 and add equations together:
It falls to III
The answer is C
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Final answer:
The solutions to the problems are: 2) (2,1), 3) B, 4) B, 5) A, and 6) D. Please remember the methods used to solve each problem as understanding the approach is important for tackling similar future questions.
Explanation:
Let's solve these equations step by step:
2. Solution of the system: 7x + 5y = 19 & -7x - 2y = -16.
Add these two equations, we get 3y = 3. So y=1. Substitute y = 1 into the first equation, we find x = 2. So the solution is (2, 1) which corresponds to option (A).
3. Simplest method to solve: y = 1/2x & 2x + 3y = 28. Here, because y is already solved in the first equation, the substitution method is the easiest. The answer is (B) Substitution.
4. Solution of the system: y = -3x & 3x + 2y = 6. Substitute y = -3x into the second equation: 3x + 2(-3x) = 6. Simplify it and find x = -1. Substituting x = -1 into y = -3x yields y = 3. So, the answer is (B) (-1, 3).
5. Number of solutions: -3x + 6y = 10 & -3x + 6y = -4. These two equations are parallel and do not intersect, thus they have (A) no solution.
6. Solution's quadrant: y=x-1 & y=-3x-5. Solve these two, we find the solution falls in quadrant (D) IV.
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