Question

Using the linear combination method, what is the solution to the system of linear equations 5x+3y=-10 and -20x-7y = 15?

Option 1: (-5, 1)
Option 2: (-1,5)
Option 3: (1,-5)
Option 4: (5, -1)

Answer 1

Using the linear combination method and multiplying the first equation by 4, we cancel out the x terms when adding both given equations, which leaves us with a simple equation to find y. After finding y=-5, we substitute it back into one of the original equations to find x=1. The solution is (1, -5), which is Option 3.

Step-by-step explanation:

To solve the system of linear equations 5x+3y=-10 and -20x-7y = 15 using the linear combination method, we need to multiply the first equation by a number that allows us to eliminate one of the variables when we add or subtract the two equations. In this case, we can multiply the first equation by 4, giving us 20x + 12y = -40. Adding this to the second equation, we get:

20x + 12y = -40
-20x - 7y = 15

When we add these equations, the x terms cancel and we get:

5y = -25

Solving for y gives us y = -5. We can then substitute this value back into one of the original equations to solve for x. Using 5x + 3y = -10, we substitute y with -5:

5x + 3(-5) = -10
5x - 15 = -10
5x = 5
x = 1

The solution to the system of equations is (1, -5), which corresponds to Option 3.