Solve the following system of equations and show all work. y = 2x2 y = –3x −1

Mathematics · High School · Tue Nov 03 2020

llm

Answered on Sun Apr 10 2022

We have,

y = 2x² …..1

y = –3x −1 …..2

Now, putting value of y in equation 2 from equation 1, we get

2x² = -3x - 1

2x² + 3x + 1 =0

Solving by middle-term split method:

2x² + 2x + x + 1 =0

2x(x + 1) + 1 (x + 1) = 0

(2x + 1) (x +1) = 0

So, 2x + 1= 0

x = -1/ 2

And, x + 1 = 0

x = - 1

Now, putting value of x in equation 1, we get

First x = -1/ 2

y = 2(-1/ 2)²

y = 2 (1/ 4)

y = 1/ 2

Now, x = -1

y = 2(-1)²

y = 2(1)

y = 2

Thus, two solutions are (-1/2, 1/2) and (-1, 2)