Question

Consider the following system.

2x - 5y = 6
3x + 2y = 4
the system were to be solved using elimination, which would the be correct factors to multiply each equation by to eliminate the variable x?

Answer 1

To eliminate x in the given system of equations using elimination, you would need to multiply the first equation by 3 and the second equation by 2. This would result in the equations 6x - 15y = 18 and 6x + 4y = 8. By subtracting these two equations, you can eliminate x and solve for y. Substituting the value of y back into one of the original equations allows you to solve for x.

Step-by-step explanation:

To eliminate the variable x in the system of equations 2x - 5y = 6 and 3x + 2y = 4 using elimination, we need to multiply the two equations by different factors so that when we add or subtract them, the x terms will cancel out. We can multiply the first equation by 3 and the second equation by 2. This will give us the equations 6x - 15y = 18 and 6x + 4y = 8. Now we can subtract the two equations to eliminate x:

6x - 15y - (6x + 4y) = 18 - 8

-19y = 10

y = -10/19

Now we can substitute this value of y back into one of the original equations to solve for x. Let's use the first equation:

2x - 5(-10/19) = 6

2x + 50/19 = 6

2x = 54/19 - 50/19

2x = 4/19

x = 2/19