Are the following systems equivalent? How do you know? 2x+y= -4 7x+7y=0
5x+6y= 4 4x+2y= -4

Step-by-step explanation:

Are the following systems equivalent? How do you know?

For the equation;

2x+y= -4 ... 1

7x+7y=0 ... 2

Let us find the solution of the equation;

From 1;

y = 4 - 2x

Susbtitutw into 2;

7x + 7(4-2x) = 0

7x + 28 - 14x = 0

-7x + 28 = 0

7x = 28

x = 28/7

x = 4

Recall that y = 4-2x

y = 4 - 2(4)

y = 4 - 8

y = -4

The solution is (4, -4)

For the other equations;

5x+6y= 4 ... 1 * 1

4x+2y= -4 2 * 3

5x+6y= 4

12x+6y= -12

Subtract

5x-12x = 4 + 12

-7x = 16

x = -16/7

Since the solutions to both simultaneous equations are different, hence the systems of equations are not equivalent.

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