An approximate x-value that represents the solution to the system of equations is equal to: C. 1.5.
How to find an approximate x-value?
Since the solution to this system of equations lies between the x-values (0 and 2), we would use the iterations of successive approximation to find an approximate x-value that represents the solution to the system of equations as follows:
y = y
4ˣ⁻¹ = 1/2ˣ⁻²
Applying the laws of power, we have:
2²⁽ˣ⁻¹⁾ = 1/2ˣ⁻²
2²ˣ⁻² = 2⁻ˣ⁺²
Evaluating the powers, we have:
2x - 2 = -x + 2
2x + x = 2 + 2
3x = 4
x = 4/3
x = 1.33.
The equation would only have a solution when the x-values lies between 0 and 2.
[tex]f(x) = 4^{x-1}\\\\f(1.33) = 4^{1.33-1}\\\\f(1.33) = 4^{0.33}[/tex]
f(1.33) = 1.58.
By using x = 1.4, we have:
[tex]f(x) = 4^{x-1}\\\\f(1.4) = 4^{1.4-1}\\\\f(1.4) = 4^{0.4}[/tex]
f(1.4) = 1.74.
By using x = 1.5, we have:
[tex]f(x) = 4^{x-1}\\\\f(1.5) = 4^{1.5-1}\\\\f(1.5) = 4^{0.5}[/tex]
f(1.5) = 2.
Read more on equations here: brainly.com/question/13170908
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