Answer:
So, the solution to the system of equations is approximately:
x ≈ -21.27
y ≈ 11.55
Explanation:
5x - 3y + 82 = -59
9x - 4y - 2 = -60
5x + 2y + 42 = _47
We'll start with the first equation:
5x - 3y + 82 = -59
Subtract 82 from both sides to isolate the terms involving x and y:
5x - 3y = -59 - 82
5x - 3y = -141
Now, let's work with the second equation:
9x - 4y - 2 = -60
Add 2 to both sides:
9x - 4y = -60 + 2
9x - 4y = -58
Now, let's work with the third equation:
5x + 2y + 42 = _47
Subtract 42 from both sides:
5x + 2y = -47 - 42
5x + 2y = -89
Now, you have the following system of equations:
5x - 3y = -141
9x - 4y = -58
5x + 2y = -89
You can use various methods to solve this system, such as substitution or elimination. Let's use the elimination method to find a solution:
First, multiply the third equation by 2 to make the coefficients of y in the first and third equations cancel each other out when added:
2(5x + 2y) = 2(-89)
10x + 4y = -178
Now, we can add the first equation and the modified third equation to eliminate y:
(5x - 3y) + (10x + 4y) = (-141) + (-178)
15x = -319
Now, divide both sides by 15 to solve for x:
15x/15 = (-319)/15
x = -319/15
Simplify the fraction:
x = -21.27 (rounded to two decimal places)
Now that we have the value of x, we can substitute it into one of the original equations to solve for y. Let's use the first equation:
5x - 3y = -141
5(-21.27) - 3y = -141
-106.35 - 3y = -141
Now, add 106.35 to both sides:
-3y = -141 + 106.35
-3y = -34.65
Finally, divide by -3 to find y:
y = -34.65 / -3
y = 11.55 (rounded to two decimal places)
So, the solution to the system of equations is approximately:
x ≈ -21.27
y ≈ 11.55