To solve this system of equations, we can start by isolating x and y in the first equation:
log√2 (x+y) = 2
Rewrite the equation using the property of logarithms:
√2^2 = x + y
Simplify:
2 = x + y
Now we can use this simplified equation to substitute x in the second equation:
3^x * 7^x = 21
Rewrite using exponents:
(3*7)^x = 21
21^x = 21
Since 21 = 3 * 7, we can rewrite the equation as:
(37)^x = 37
This gives us:
x = 1
Substitute x=1 back into the simplified equation we found earlier:
2 = x + y2 = 1 + yy = 1
Therefore, the solution to the system of equations is x = 1, y = 1.
To solve this system of equations, we can start by isolating x and y in the first equation:
log√2 (x+y) = 2
Rewrite the equation using the property of logarithms:
√2^2 = x + y
Simplify:
2 = x + y
Now we can use this simplified equation to substitute x in the second equation:
3^x * 7^x = 21
Rewrite using exponents:
(3*7)^x = 21
Simplify:
21^x = 21
Since 21 = 3 * 7, we can rewrite the equation as:
(37)^x = 37
This gives us:
x = 1
Substitute x=1 back into the simplified equation we found earlier:
2 = x + y
2 = 1 + y
y = 1
Therefore, the solution to the system of equations is x = 1, y = 1.