Algebra homework

Question

What is the x-coordinate of one solution to the following system?

y=5x^2-50x+126

y=2x^2-16x+35

A. 13.67

B. 35.33

C. 7.00

D. 20.52

Answer 1

Substitute one equation for y:

5x^2-50x+126=2x^2-16x+35

after simplification we get 3x^2-34x+91=0

we can factor the left hand side and get (x-7)(3x-13)=0

this means x=7 or x=13/3

So C is correct

Since this is a multiple choice question, another way to solve it is to substitute ABCD for x to see which one  makes the equality in the equation true.

Answer 2

Set the equations = to each other, combine like terms by adding/subtracting on both sides of the equation, so that the new equation is in the form ax² + bx + c = 0..

3x² - 34x + 91 = 0

You may use the quadratic equation to solve. Or try plugging in the values in choices A-D.

Or factor

(x - 7)(3x - 13) = 0, giving x = 7 and x = 13/3. So choice C works.