Question

The system of equations can be solved using linear combination to eliminate one of the variables.

2x − y = −4 → 10x − 5y = −20
3x + 5y = 59 → 3x + 5y = 59
13x = 39
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

Answer 1

Answer:

The equation 3x + 5y = 59 can be replaced by 13x = 39.

Step-by-step explanation:

The given system of equation is

$2x-y=-4$              .... (1)

$3x+5y=59$              .... (2)

Multiply equation 1 by 5.

$10x-5y=-20$              .... (3)

Now, add equation (2) and (3).

$13x=39$                   ....(4)

$x=3$

Substitute x=3 in equation (1).

$2(3)-y=-4$              .... (1)

$y=10$

The solution of the system is (3,10).

If the equation 2 is replaced by equation 4, then the system of equation is

$2x-y=-4$

$13x=39$

On solving both equations we get.

$x=3$

$y=10$

The solution of the system is (3,10).

Since the solution of the system remains same, therefore equation 3x + 5y = 59 can be replaced by 13x = 39.

Answer 2

The answer on edgenuity is option 4, (D) or 13x = 39

The solution of the system is (3,10).

Since the solution of the system remains same, therefore equation 3x + 5y = 59 can be replaced by 13x = 39.