Solving a system of equations

[TTSDBTJJ]

The math class I am taking is online, and one of the downsides is it is hard to contact the teacher for help. There is an online help center, but unfortunately no teachers are available for the next few days. I have attempted to solve the system of equations but get messed up every time. The problem is that the videos I have watched for solving a system of equations give them in the form similar to this-
2x+y=9
3x-y=16
The system that I need to solve is slightly different.
y=4x+12
y=4x²+4
I do not really have any work to show as the times I have tried it ends up something like x+2= x². I would appreciate any assistance in understanding how to solve a system of equations. Thanks in advance! =)

 

[HallsofIvy]

The math class I am taking is online, and one of the downsides is it is hard to contact the teacher for help. There is an online help center, but unfortunately no teachers are available for the next few days. I have attempted to solve the system of equations but get messed up every time. The problem is that the videos I have watched for solving a system of equations give them in the form similar to this-
2x+y=9
3x-y=16
The system that I need to solve is slightly different.
y=4x+12
y=4x²+4
I do not really have any work to show as the times I have tried it ends up something like x+2= x². I would appreciate any assistance in understanding how to solve a system of equations. Thanks in advance! =)

Since both 4x+ 12 and \(\displaystyle 4x^2+ 4\) are both equal to y, they are equal to each other- \(\displaystyle 4x^2+ 4= 4x+ 12\) which, subtracting 4x+ 12 from both sides is the same as the quadratic equation \(\displaystyle 4x^2- 4x- 8= 0\). Now you can divide through by 4 to get the slightly simpler equation \(\displaystyle x^2- x- 2= 0\) which is equivalent to the equation.

Do you not know how to solve quadratic equations? That, in fact, factors with integer coefficients.

 

[JeffM]

The math class I am taking is online, and one of the downsides is it is hard to contact the teacher for help. There is an online help center, but unfortunately no teachers are available for the next few days. I have attempted to solve the system of equations but get messed up every time. The problem is that the videos I have watched for solving a system of equations give them in the form similar to this-
2x+y=9
3x-y=16
The system that I need to solve is slightly different.
y=4x+12
y=4x²+4
I do not really have any work to show as the times I have tried it ends up something like x+2= x². This of course is just a different arrangement of the solution that Halls of Ivy got. I would appreciate any assistance in understanding how to solve a system of equations. You did the work of reducing the system of simultaneous equations to a single equation perfectly. Unfortunately, one of the equations was not linear so when you reduced the system to a single equation you found CORRECTLY that it is still not linear. You are not having a problem with solving simultaneous equations. You are having a problem with solving a single non-linear equation

There are a number of ways to solve a quadratic equation. Have you studied quadratics yet?