Checking Intersection point from two student input equations

I am trying to build a challenge creator where students would create two linear slope-intercept form equations and then the students determine the coordinate point where lines intersect to solve the challenge. Here is what I have so far

I can’t figure out how to get Desmos to determine the point of intersection from the student input equations and then check that against the student answer on the submission slide. Thank you for your help!

You can utilise the regression tool to help you find the point of intersection. For instance, f(x_1)~g(x_1) will find a value x_1 that represents the x-ordinate of the point of intersection. Then y_1=f(x_1) will find the y.

Example: [Copy of] Challenge Creator - Linear systems • Activity Builder by Desmos

Thank you so much for your help, here is the final product that I came up with