Final answer:
To find the approximate solution of the given system of equations, 8x + 3y = 9 and 3x - 5y = 20, we can use the method of elimination. The approximate solution is (2.14, -1.99).
Step-by-step explanation:
To find the approximate solution of the given system of equations, 8x + 3y = 9 and 3x - 5y = 20, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply the first equation by 5 and the second equation by 3 to make the coefficients of y match:
40x + 15y = 45
9x - 15y = 60
Add the two equations together:
49x = 105
Divide both sides by 49:
x = 105/49
Substitute this value of x into either equation to find y:
Using the first equation, we have:
8*(105/49) + 3y = 9
From here, we can solve for y:
y = (9 - 8*(105/49))/3
Simplifying this expression gives us y = -1.99.
Therefore, the approximate solution to the system of equations is (105/49, -1.99). When rounded to two decimal places, this is approximately (2.14, -1.99).