What is y-6=x^2-3x,x+2y=2 ?

The solution to y-6=x^2-3x,x+2y=2 is

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y-6=x^2-3x,x+2y=2

y - 6 = x^{2} - 3 x, x + 2 y = 2

(x = \frac{5}{4} - i \frac{55}{4}, x = \frac{5}{4} + i \frac{55}{4}, y = \frac{3}{8} + i \frac{55}{8} y = \frac{3}{8} - i \frac{55}{8})

Solution steps

[y - 6 = x^{2} - 3 x x + 2 y = 2]

Isolate

x

for

x + 2 y = 2 : x = 2 - 2 y

Plug the solutions

x = 2 - 2 y

into

y - 6 = x^{2} - 3 x

For

y - 6 = x^{2} - 3 x

, subsitute

x

with

2 - 2 y : y = \frac{3}{8} + i \frac{55}{8}, y = \frac{3}{8} - i \frac{55}{8}

Plug the solutions

y = \frac{3}{8} + i \frac{55}{8}, y = \frac{3}{8} - i \frac{55}{8}

into

x + 2 y = 2

For

x + 2 y = 2

, subsitute

y

with

\frac{3}{8} + i \frac{55}{8} : x = \frac{5}{4} - i \frac{55}{4}

For

x + 2 y = 2

, subsitute

y

with

\frac{3}{8} - i \frac{55}{8} : x = \frac{5}{4} + i \frac{55}{4}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

y - 6 = x^{2} - 3 x, x + 2 y = 2

are

(x = \frac{5}{4} - i \frac{55}{4}, x = \frac{5}{4} + i \frac{55}{4}, y = \frac{3}{8} + i \frac{55}{8} y = \frac{3}{8} - i \frac{55}{8})

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

x^{2} - 31 x + 184 = 0, y^{2} - 49 y + 600 = 0

x^{2} + y^{2} = 2, 5 y - x + 7 = 0

x + y = 3, \neg 65 x + 119 y = 249

5 x - 6 y = 20, 4 x - 3 \frac{y}{4} x - 3 y = 23