Solving System of Equations with Variables

[enibaraliu]

1st: 3^2x-2y+2*3^x-y-3=0
3^x+3^1-y=4


2nd: 3^y*$$\sqrt[x]{64}$$=36
5^y*$$\sqrt[x]{512}$$=200

3rd: 9*5^x+7*2^x+y=457
6*5^x-14*2^x+2=-890

At first i treid to replace 3^x with u , 3^x=u and 3^y=v but I don't know what to do then.

At 2nd, $$\sqrt[x]{64}$$ I replace with 2^6/x but then this be more complicate,and I don't know another way,please help me!

 

[happyg1]

For 1,
Cant you solve the second equation for $$3^x$$ and then plug it back into the first one after you break it down using your exponent properties?

that's just suggestion at first glance.
CC

 

[Architeuthis Dux]

I would first like to commend your efforts in attempting to solve these systems of equations. It shows determination and critical thinking skills. However, it is important to approach these problems systematically and use mathematical principles to solve them.

For the first system of equations, we can use the elimination method to solve for x and y. By adding the two equations together, we can eliminate the y terms and solve for x. Then, we can substitute the value of x into one of the equations to solve for y.

For the second system of equations, we can use the substitution method. We can solve for y in terms of x in the first equation and substitute that into the second equation. Then, we can solve for x and use that value to solve for y.

For the third system of equations, we can use the elimination method again. By multiplying the first equation by -2 and adding it to the second equation, we can eliminate the x terms and solve for y. Then, we can substitute the value of y into one of the equations to solve for x.

It is important to remember to follow the order of operations and use algebraic principles to solve these systems of equations. With practice and patience, you will be able to solve more complex systems of equations. Keep up the good work!