Whst is the solution of the system use elimination
-18.6x + 17.2y = 90.2
14.2x + 3.4y = 35.8
To solve the system of equations using elimination, we can multiply the second equation by -1 in order to cancel out the x term when combined with the first equation.
-18.6x + 17.2y = 90.2
-14.2x - 3.4y = -35.8 (multiply by -1)
Next, we can add the two equations together to eliminate the x term:
-18.6x + 17.2y = 90.2
+ (-14.2x - 3.4y = -35.8)
This gives us:
-32.8y = 54.4
Now, we can solve for y by dividing both sides of the equation by -32.8:
y = 54.4/(-32.8)
y = -1.66
Now, we can substitute this value of y back into either of the original equations to find the value of x. Let's use the first equation:
-18.6x + 17.2(-1.66) = 90.2
Simplifying this equation:
-18.6x - 28.392 + 28.392 = 90.2 + 28.392
-18.6x = 118.592
Finally, we can solve for x by dividing both sides of the equation by -18.6:
x = 118.592/(-18.6)
x = -6.37
Therefore, the solution to the system of equations is x = -6.37 and y = -1.66.