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

see explanation

Step-by-step 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)

step-by-step explanation: