Question

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

y=x^2-x-42


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Answer 1

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

Answer 2

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)