The image shows the following system of equations:

$3^x - 2^{x^2} = 10$ $2^x - 3^{x^2} = 2$

These are non-linear exponential equations, which are generally complex to solve algebraically. A common approach is to look for specific values of $x$ that satisfy both equations through trial, error, or numerical methods.

Let me first try some common integer values for $x$ and see if they work for both equations.

Equation 1: $3^x - 2^{x^2} = 10$

Testing $x = 2$: $3^2 - 2^{2^2} = 9 - 16 = -7 \quad \text{(not valid)}$

Testing $x = 3$: $3^3 - 2^{3^2} = 27 - 512 = -485 \quad \text{(not valid)}$

Testing $x = 1$: $3^1 - 2^{1^2} = 3 - 2 = 1 \quad \text{(not valid)}$

Let me now check if solving these numerically might be a better approach. Shall I proceed with this?