Question

Y=2x^2 -7x+4 and y=11-2x

Answer 1

Explanation:

First, we need to equate the two equations to each other. We do this by setting Y of the two equations to equal each other.

Y = 2x^2 - 7x + 4 = 11 - 2x

Now we need to simplify. We can subtract 4 from both sides which will eliminate the 4 from the left side and will add 4 to the right side:

2x^2 - 7x = 7 + 2x

Now we can combine the two x terms on the left side and subtract the 2x on the right side

2x^2 - 9x = 7

Now we can divide both sides by 2 to solve for x.

x^2 - 4.5x = 3.5

Now we subtract 3.5 from both sides to isolate the x^2

x^2 - 4.5x - 3.5 = 0

Now we use the quadratic equation to solve for x.

x = {4.5 +/- sqrt(4.5^2 - 4(1)(-3.5))}/(2(1))

x = {4.5 +/- sqrt(20.25 + 14) }/2

x = (4.5 +/- sqrt(34.25))/2

x = (4.5 +/- 5.8626)/2

x = 4.5/2 +/- 5.8626/2

x = 2.25 +/- 2.9313

Therefore, x = 2.25 and 5.1813

Answer 2

(- 1, 13 ) , (3.5, 4 )

Explanation:

y = 2x² - 7x + 4 → (1)

y = 11 - 2x → (2)

substitute y = 2x² - 7x + 4 into (2)

2x² - 7x + 4 = 11 - 2x ( add 2x to both sides )

2x² - 5x + 4 = 11 ( subtract 11 from both sides )

2x² - 5x - 7 = 0 ← in standard form

(x + 1)(2x - 7) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

2x - 7 = 0 ( add 7 to both sides )

2x = 7 ( divide both sides by 2 )

x = 3.5

substitute these values into (2) for corresponding values of y

x = - 1 : y = 11 - 2(- 1) = 11 + 2 = 13

x = 3.5 : y = 11 - 2(3.5) = 11 - 7 = 4

solutions are (- 1, 13) and (3.5, 4 )