Determine the equivalent system for the given system of equations.

4x − 5y = 2
3x − y = 8

4x − 5y = 2
10x − 7y = 18
4x − 5y = 2
3x − 8y = 4
4x − 5y = 2
10x + 3y = 15
4x − 5y = 2
7x + 6y = 10

A) 4x − 5y = 2

10x − 7y = 18

Step-by-step explanation:

4x − 5y = 2 --> (1)

3x − y = 8 --> (2)

(1) + 2(2)

4x - 5y = 2

6x - 2y = 16

10x - 7y = 18

Heya!

Lets solve for the system given in the question.

4x − 5y = 2

3x − y = 8

Rewrite both equations.

Solve 3x − y = 8 for y.

3x - y = 8

~Subtract 3x to both sides

3x - y - 3x = 8 - 3x

~Simplify

-y = -3x + 8

~Divide -1 to both sides

-y/-1 = -3x+8/-1

~Simplify

y = 3x - 8

Substitute 3x - 8 for y in 4x − 5y = 2

4x - 5(3x - 8) = 2

~Simplify

-11x + 40 = 2

~Subtract 40 to both sides

-11x + 40 - 40 = 2 - 40

~Simplify

-11x = -38

~Divide -11 to both sides

-11x/-11 = -38/-11

~Simplify

x = 38/11

Substitute 38/11 for x in y = 3x - 8

y = 3(38/11) - 8

~Simplify

y = 26/11

The solution to the system is (38/11, 26/11).

The answer is A. 4x − 5y = 2, 10x − 7y = 18

Lets solve for the system given in the answer.

4x − 5y = 2

10x − 7y = 18

Rewrite both equations.

Solve 4x − 5y = 2 for x.

4x − 5y = 2

~Add 5y to both sides

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

~Simplify

4x = 2 + 5y

~Divide 4 to both sides

4x/4 = 2+5y/4

~Simplify

x = 1/2 + 4/5y

Substitute 1/2 + 4/5y for x in 10x − 7y = 18

10(1/2 + 4/5y) − 7y = 18

~Simplify

11/2y + 5 = 18

~Subtract 5 to both sides

11/2y + 5 - 5 = 18 - 5

~Simplify

11/2y = 13

~Divide both sides by 11/2

11/2y ÷ 11/2 = 13 ÷ 11/2

~Simplify

y = 26/11

Substitute 26/11 for in x = 1/2 + 4/5y

x = 1/2 + 4/5(26/11)

~Simplify

38/11

The solution to the system is (38/11, 26/11).

That makes it the correct answer.

Best of Luck!

c is the answer

step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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