Question

Consider the system of equations. 5x + 2y = 6, 10x + 4y = 12 Which equation is equivalent to the first equation of the system and can be used to solve the system using the linear combination method? Which answer describes the number of solutions to the system of equations?

Answer 1

part 1 is -10x-4y=-12 part 2 is infinitely many solution

Answer 2

Answer: You have infinite solutions to the system, and those can be obtained by the relation y = 3 - (5/2)*x where you can give any value for x.

Explanation:

The equations that we have are:

5x + 2y = 6 and 10x + 4y = 12

First, you can see that the second equation is equal to the first equation multiplied by a factor of 2:

2*(5x + 2y) = 2*6

10x + 4y = 12

this means that the equations are not linear independent, so in this case, we have only one equation that has information and two variables, because we have fewer equations than variables, we have infinite possible solutions of our system.

for solving this we can do:

5x + 2y = 6

2y = 6 - 5x

y = 3 - (5/2)*x

now, you an give value to x, and from this, you get the value of y.