Question

Solve the system of equations. 13x−y=90

Answer 1

Lets solve the system of equations step by step.
$13x-y=90$ equation (1)
$y=x^2-x-42$ equation (2)

Step 1. Solve for $y$ in equation (1)
$13x-y=90$
$-y=90-13x$
$y=13x-90$ equation (3)

Step 2. Replace equation (3) in equation (2) and solve for $x$:
$y=x^2-x-42$
$13x-90=x^2-x-42$
$x^2-14x+48=0$
$(x-6)(x-8)=0$
$x=6$ equation (4)
$x=8$ equation (5)

Step 3. Replace equation (4) and equation (5) in equation (3)
(4) in (3)
$y=13x-90$
$y=13(6)-90$
$y=-12$

(5) in (3)
$y=13x-90$
$y=13(8)-90$
$y=14$

We can conclude that the solutions of our system of equations are (6,-12) and (8,14)

Answer 2

Solving for the solutions of two equations is simply done by substitution.

So  the easiest way is to;
13x−y=90 
y = 13x - 90

Substitute this to
y = x^2 - x - 42
13x - 90 = x^2 - x - 42
0 = x^2 - 14x + 48

Factoring the equation we get;
 0 = (x-8)(x-6)

So the solutions are 6 and 8