Respuesta :

cerverusdante
Lets solve the system of equations step by step.
[tex]13x-y=90[/tex] equation (1)
[tex]y=x^2-x-42[/tex] equation (2)

Step 1. Solve for [tex]y[/tex] in equation (1)
[tex]13x-y=90[/tex]
[tex]-y=90-13x[/tex]
[tex]y=13x-90[/tex] equation (3)

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

Step 3. Replace equation (4) and equation (5) in equation (3)
(4) in (3)
[tex]y=13x-90[/tex]
[tex]y=13(6)-90[/tex]
[tex]y=-12[/tex]

(5) in (3)
[tex]y=13x-90[/tex]
[tex]y=13(8)-90[/tex]
[tex]y=14[/tex]

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