Question

Solve the system of equations.
y-10x=5
y=x^2+7x+5

Answer 1

see explanation

Explanation:

Given the 2 equations

y - 10x = 5 → (1)

y = x² + 7x + 5 → (2)

From (1) express y in terms of x by adding 10x to both sides

y = 10x + 5 → (3)

Substitute y = 10x + 5 into (2)

10x + 5 = x² + 7x + 5 ( subtract 10x + 5 from both sides )

0 = x² - 3x ( take out common factor of x ), hence

x(x - 3) = 0

Equate each factor to zero and solve for x

x = 0

x - 3 = 0 ⇒ x = 3

Substitute these values into (3) for corresponding values of y

x = 0 : y = 0 + 5 = 5 ⇒ (0, 5 ) is a solution

x = 3 : y = 30 + 5 = 35 ⇒ (3, 35 ) is a solution

Solutions are (0, 5) , (3, 35)

Answer 2

x = 0,3

Explanation:

y-10x=5 move -10x to the other side to get y by itself

y=10x+5 then you would substitute this equation into the other equation where you see y

10x+5=x^2+7x+5 move everything to one side

0=x^2+7x+5-10x-5 combine like terms

0=x^2-3x factor

0 = x(x-3) set each equal to zero

x=0

x-3 = 0 add 3 to both sides

x = 3

the answer is x=0 and x=3