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?
a.2x – y = –4
b.10x – 5y = –20
c.7x = 39
d.13x = 39

13x = 39

Step-by-step explanation:

Given system of equations,

2x - y = - 4 -----(1)

3x + 5y = 59 ----(2),

Equation (2) + 5 × equation (1),

We get,

13x = 39 ⇒ x = 3

From equation (1),

2(3) - y = - 4 ⇒ 6 - y = -4 ⇒ y = 10

Thus, the solution of the given system is (3, 10),

Now, when the equation (2) is replaced by 2x - y = -4,

System of equations would be,

2x − y = −4

2x − y = −4

∵ both equation shows the same line,

Hence, the system has infinitely many solution,

When the equation (2) is replaced by 10x - 5y = -20,

System of equations would be,

2x - y = -4,

10x − 5y = −20,

Again both lines shows the same line ( because ),

Hence, the system has infinitely many solution,

When the equation (2) is replaced by 7x = 39,

System of equations would be,

2x - y = -4,

7x = 39,

Then the solution would be (5,571, 15.143)

When the equation (2) is replaced by 13x = 39,

System of equations would be,

2x - y = -4,

13x = 39

Then the solution of the system would be (3, 10).

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

8+10

step-by-step explanation:

you multiply 4 by 2 and 5 by 2