Answer:
The approximate solution to the system of equations is x ≈ 0.9103 and y ≈ 4.5515.
Explanation:
To solve the linear-quadratic system of equations algebraically, we need to set the two expressions for y equal to each other:
y = 5x
y = 3^x
Setting these equations equal to each other:
5x = 3^x
Now, to solve for x, we need to isolate the variable x. One way to do this is to take the logarithm of both sides. Let's use the natural logarithm (ln):
ln(5x) = ln(3^x)
Now, we can use the properties of logarithms to simplify the equation:
ln(5x) = x * ln(3)
Next, isolate x:
x = ln(5x) / ln(3)
Since the x appears on both sides of the equation, it's not straightforward to find the exact value of x algebraically. We can use numerical methods or calculators to find an approximate value for x:
x ≈ 0.9103
So, the approximate solution to the system of equations is x ≈ 0.9103. To find the corresponding value of y, we can use either of the original equations. Let's use the first equation:
y = 5x
y ≈ 5 * 0.9103
y ≈ 4.5515