alfred tried to solve the system of equations shown below. he concluded that the system has an infinite number of solutions. which is the best evaluation of alfred's conclusion? a. he is incorrect. for any positive value of , the corresponding value of is negative, which means the system has no solution. b. he is correct. both equations describe lines that have infinitely many solutions. c. he is incorrect. if the first equation is multiplied by 4 and added to the second equation, the result is , which leads to exactly one solution. d. he is correct. if the first equation is multiplied by 4 and subtracted from the second equation, the result is , which means the system has an infinite number of solutions.

is a straight line (unless both a and b are zero), so such an equation is called a linear equation in variables x and y. There are three possible types of solutions to a set of linear equations.

Unique Solution: A system of linear equations has a solution if the graphs intersect at a point.
No Solution: If the graph is parallel, the system of linear equations has no solution.
Infinitely Many Solutions: There are infinitely many solutions to a system of linear equations if the graph is exactly the same straight line.

given system of equations is

2x - y = 4 --(1)

and 5x + 4y = -10 ---(2)

comparing the above equations with linear system , a1 x + b1 y = c1 and a2 x + b2y = c2

we get, a1 = 2 , a2= 5 , b1 = -1 , b2= 4 , c1= 4 ,

c2= -10

Now, the ratio are

a1/a2 = 2/5 ; b1/b2 = -1/4 ; c1/c2= -4/10 = 2/5

=> a1/a2 not equal to b1/ b2

therefore the given system of equations has unique solution.

Now , we find the soltion of given system using Elimination method,

multipling equation (1) by 4 to making same cofficient of y in both equations of system we get

8x - 4y = 16 --(3) and 5x +4y = -10

adding equation (2) from (3) we get,

8x -4y + 5x + 4y = 16 -10 => 13x = 6 => x = 6/13

putting this value of x in (1)

2×6/13 - y = 4 => y = 12/13-4 = -40/13

Hence , unique solution for given system of equations is x= 6/13 , y = -40/13.

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Complete Question:

Alfred tried to solve the system of equations shown below..

2x - y = 4 and 5x + 4y = -10

He concluded that the system has an infinite number of solutions. Which is the BEST evaluation of Alfred's conclusion?

He is correct. Both equations describe lines that have infinitely many solutions.

He is correct. If the first equation is multiplied by 4 and subtracted from the second equation, the result is -3x +8y = -14 , which means the system has an infinite number of solutions.

He is incorrect. For any positive value of , the corresponding value of is negative, which means the system has no solution.

He is incorrect. If the first equation is multiplied by 4 and added to the second equation, the result is 13x = 6 , which leads to exactly one solution.