Math  /  Algebra

Question3. If (13)x+y=243\left(\frac{1}{3}\right)^{x+y}=243 and log2(2yx)=2\log _{2}(2 y-x)=2, calculate the values of xx and yy algebraically.

Studdy Solution
Now, we have the system of equations:
1. x+y=5x+y = -5
2. 2yx=42y-x = 4

Add the two equations to eliminate xx:
(x+y)+(2yx)=5+4(x+y) + (2y-x) = -5 + 4
Simplifying, we get:
3y=13y = -1
Solve for yy:
y=13y = -\frac{1}{3}
Substitute y=13y = -\frac{1}{3} back into the first equation x+y=5x+y = -5:
x13=5x - \frac{1}{3} = -5
Solving for xx, we find:
x=5+13x = -5 + \frac{1}{3} x=153+13x = -\frac{15}{3} + \frac{1}{3} x=143x = -\frac{14}{3}
The values of xx and yy are:
x=143,y=13 x = -\frac{14}{3}, \quad y = -\frac{1}{3}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord