how to solve system of equation

Question

{y=x^2+2x-7

{x-y=-5

 

 

Answer 1

y = x² + 2x - 7         eq1

x - y = -5                 eq2

 

 

We can substitute eq2 into eq1.  eq1 will be in terms of x.  Before we substitute, lets solve for y from eq2.

 

-y = -x - 5

 

y = x + 5

 

 

Now, we can substitute.

 

x + 5 = x² + 2x - 7

 

Move all the terms on the left side to the right side by subtract x and subtracting 5 on both sides of equation.  This will make the left side of equation equal to zero.

 

0 = x² + x - 12

 

 

Factor the left right side of equation.

 

0 = (x + 4)(x - 3)

 

x = -4        and         x = 3

 

We have two solutions of x.  Next, substitute these two values respectively into eq2.

 

y = -4 + 5            and           y = 3 + 5

 

y = 1                    and           y = 8

 

We have two solutions of y because we have two solutions of x.  Therefore, we will have two solutions sets.

 

(-4, 1)      and       (3, 8)