What is 3x+y=4,2y^5x+3y=78 ?

The solution to 3x+y=4,2y^5x+3y=78 is

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3x+y=4,2y^5x+3y=78

3 x + y = 4, 2 y^{5} x + 3 y = 78

(x = 0.03733 \dots, x = 0.57188 \dots, y = 3.88800 \dots y = 2.28435 \dots)

Solution steps

[3 x + y = 4 2 y^{5} x + 3 y = 78]

Isolate

x

for

3 x + y = 4 : x = \frac{4 - y}{3}

Plug the solutions

x = \frac{4 - y}{3}

into

2 y^{5} x + 3 y = 78

For

2 y^{5} x + 3 y = 78

, subsitute

x

with

\frac{4 - y}{3} : y \approx 3.88800 \dots, y \approx 2.28435 \dots

Plug the solutions

y = 3.88800 \dots, y = 2.28435 \dots

into

3 x + y = 4

For

3 x + y = 4

, subsitute

y

with

3.88800 \dots : x = 0.03733 \dots

For

3 x + y = 4

, subsitute

y

with

2.28435 \dots : x = 0.57188 \dots

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

3 x + y = 4, 2 y^{5} x + 3 y = 78

are

(x = 0.03733 \dots, x = 0.57188 \dots, y = 3.88800 \dots y = 2.28435 \dots)

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