Solve the system

Question

y=3x+1

y=x^2+1

Type your answer as ordered pairs (x,y) with the order: from the smallest value of x to the largest

Answer 1

y = 3x + 1           eq1

y = x² + 1           eq2

 

 

Substitute eq1 into eq2.

 

3x + 1 = x² + 1

 

 

Subtract 3x and subtract 1 on both sides of equation.

 

0 = x² - 3x

 

 

Factor out the right side of the equation.

 

0 = x(x - 3)

 

x = 0         and         x = 3

 

 

Substitute these x values into eq2.

 

y = (0)² + 1           and         y = (3)² + 1

y = 1                     and          y = 10

 

 

The ordered pairs from the smallest value of x are  (0,1) and (3,10).