Question

1. instructions: (1) no cell - phones during the test. (2) show your work for full credit. name: first name, last name section a: knowledge and understanding (1) identify and understand key words between the graph and the point of intersection for the graph below. a. ( - 6, - 1) b. (0,7) c. ( - 1, - 6) d. (5,0) 2. decide whether the following linear system has one solution, no solution, or infinite number of solutions. y = 3x+2 12x - 4y=-8 a. one solution b. no solution c. infinite number of solutions d. none of the above 3. how many solutions are there to the following linear system? y = 3x+2 12x - 4y = 8 a. one solution b. no solution c. infinite number of solutions d. none of the above 4. which point is a solution for the following linear system? x - 2y = 4 ( - 1, - 2) b. (1, - 2) c. (2, - 1) d. ( - 2, - 1) 5. solve the linear system by substitution or elimination. 2x + 7y = 86 4x + 5y = 42 a. b. c. d. 6. match the word or phrase with its definition. a. slope b. point - slope form of a line c. method of intersection d. intercept 7. when two lines cross at the point (x,y), the point is called the point of intersection. a. true b. false 8. a solution method in which a variable is replaced in one equation with an equivalent expression from another equation is called substitution. a. true b. false 9. when two lines are parallel, this means that their equations are equivalent. a. true b. false 10. when two lines are perpendicular, their slopes are negative reciprocals of each other. a. true b. false

Explanation:

Step1: Identify the problem type

This is about linear - systems and graphing.

Step2: Analyze linear - system solutions

For a linear system \(y = 3x+2\) and \(y=-4x - 5\), we can find the solution by setting the two equations equal to each other: \(3x + 2=-4x-5\).

Step3: Solve for \(x\)

Add \(4x\) to both sides: \(3x+4x + 2=-5\), so \(7x+2=-5\). Then subtract 2 from both sides: \(7x=-7\), and \(x = - 1\).

Step4: Solve for \(y\)

Substitute \(x=-1\) into \(y = 3x+2\), we get \(y=3\times(-1)+2=-3 + 2=-1\). So the solution is \((-1,-1)\).

Step5: Analyze number of solutions

The two lines \(y = 3x+2\) and \(y=-4x - 5\) have different slopes (3 and - 4), so they intersect at exactly one point, which means there is 1 solution.

Answer:

The solution of the linear - system \(y = 3x+2\) and \(y=-4x - 5\) is \((-1,-1)\) and the number of solutions of the system is 1.