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).