What is y=x^2-2x+3,y=-5x+1 ?

The solution to y=x^2-2x+3,y=-5x+1 is

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y=x^2-2x+3,y=-5x+1

y = x^{2} - 2 x + 3, y = - 5 x + 1

(x = - 1, x = - 2, y = 6 y = 11)

Solution steps

[y = x^{2} - 2 x + 3 y = - 5 x + 1]

Subtract the equations

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

y - y = x^{2} - 2 x + 3 - (- 5 x + 1)

Simplify

0 = x^{2} + 3 x + 2

Solve

0 = x^{2} + 3 x + 2 : x = - 1, x = - 2

Plug the solutions

x = - 1, x = - 2

into

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

For

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

, subsitute

x

with

- 1 : y = 6

For

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

, subsitute

x

with

- 2 : y = 11

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

y = x^{2} - 2 x + 3, y = - 5 x + 1

are

(x = - 1, x = - 2, y = 6 y = 11)

2 x + 5 \frac{y}{x} y = 6, 4 x - 5 \frac{y}{x} y = - 3

3 x + 5 y = 3, 2 x^{1} y = - 5

x - 1 = 1, x^{3} - y^{3} = 7

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

\frac{1}{2 ^{x}} + \frac{2}{3 ^{y}} = 10, \frac{3}{2 ^{x}} + \frac{7}{3 ^{y}} = 33