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!

step-by-step explanation: