To solve the given system of equations using the elimination method, follow these steps:
Step 1: Multiply the equations by suitable numbers to make the coefficients of one of the variables opposites in the two equations. In this case, let's choose to eliminate the variable "y." Looking at the coefficients of "y" in both equations, we can multiply the first equation by 8 and the second equation by -7.
8*(5x - 7y) = 8*(-16) [Multiply the first equation by 8]
-7*(2x + 8y) = -7*(26) [Multiply the second equation by -7]
This will give us:
40x - 56y = -128
-14x - 56y = -182
Step 2: Add the two equations obtained in step 1. By doing this, we eliminate the variable "y."
(40x - 56y) + (-14x - 56y) = -128 + (-182)
40x - 56y - 14x - 56y = -310
(40x - 14x) + (-56y - 56y) = -310
26x - 112y = -310
So, the new equation after adding both equations is: 26x - 112y = -310.
Step 3: Solve the new equation obtained in step 2 for the remaining variable. In this case, let's solve for "x."
26x - 112y = -310
To isolate the "x" term, we can move the "-112y" term to the right side of the equation by adding 112y to both sides:
26x = 112y - 310
Next, divide both sides of the equation by 26 to solve for "x":
x = (112y - 310)/26
Step 4: Substitute the value of "x" obtained in step 3 into either of the original equations to solve for "y." Let's substitute it into the first equation:
5x - 7y = -16
5((112y - 310)/26) - 7y = -16
Now simplify and solve the equation for "y."