Plz help me to solve this system of equation.
2^x+3^y=17
2^x+2+3^y+1=5
Represent 2 ^ x with p and 3 ^y with q . .p + q =17. And 2^ x+2 = 2^x X 2^2 =4p + 3 ^ y+1 =3^y x 3^1 =3q. . Solve simultaneously. P +q=17. . 4p + 3q = 5. . . . q =63 . P = -46
To solve this system of equations, we will use the method of substitution. Here are the steps to find the values of x and y:
Step 1: Rewrite the equations in terms of a single variable.
Let's rewrite the first equation: 2^x + 3^y = 17 -----(Equation 1)
And the second equation: 2^x + 2 + 3^y + 1 = 5 -----(Equation 2)
Step 2: Isolate one variable in terms of the other.
From Equation 2, we can isolate 2^x by subtracting 3 from both sides and obtain: 2^x = 5 - 2 - 3^y - 1
Simplifying Equation 2 further, we get: 2^x = 2 - 3^y -----(Equation 3)
Step 3: Substitute Equation 3 into Equation 2.
Since both Equation 2 and Equation 3 represent 2^x, we can substitute Equation 3 into Equation 2 as follows:
2 - 3^y + 3^y + 1 = 5
Simplifying the equation, we get: 3^y = 4 -----(Equation 4)
Step 4: Solve Equation 4 for y.
Taking the logarithm (base 3) of both sides of Equation 4, we get: y = log₃(4)
Step 5: Substitute the value of y into Equation 1 to find x.
Using Equation 1, let's substitute log₃(4) for y:
2^x + 3^(log₃(4)) = 17
Since 3^(log₃(4)) can be rewritten as 4, the equation becomes:
2^x + 4 = 17
Subtracting 4 from both sides, we get: 2^x = 13
Step 6: Solve Equation 5 for x.
Taking the logarithm (base 2) of both sides of Equation 5, we get: x = log₂(13)
Therefore, the solution to the system of equations is x = log₂(13) and y = log₃(4).
SO I assume you really meant this:
2^x+3^y=17
2^(x+2)+3^(y+1)=5
changing the second equation to
4*2^x +3*3^y = 5
now multiply the first equation by 4
4*2^x+4*3^y=17*4
now subtract
4(2^x) +3*3^y=5
and the result is
4*3^y-3*3^y=17*4-5
or
3^y=63=3^2 * 7
take the log(base3) of each side
Y=2 +log3 (7)