Question

Solve the system of equations.
13x−y=90
y=x^2−x−42

Answer 1

Solve the first for y

y=13x-90 and the second is y=x^2-x-42

When there is/are solutions y=y so we can say:

x^2-x-42=13x-90  subtract 13x from both sides

x^2-14x-42=-90  add 90 to both sides

x^2-14x+48=0  expand so that it is easy to factor...

x^2-6x-8x+48=0 now factor 1st and 2nd pair of terms

x(x-6)-8(x-6)=0

(x-8)(x-6)=0

So there are two solutions, when x=6 and 8.

Using either original equation we can find the corresponding values for y.  I'll use y=13x-90 because it is easier...

y(6)=-12, y(8)=14  so the two solutions are the points:

(6,-12) and (8,14)

Answer 2

The two solution points are :  (6,-12) and (8,14)

What is system of equations ?

In mathematics, a system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions.

The given is two equation 13x - y = 90

and the second is y = x² - x -42

Solve the first equation for y

y = 13x-90

Putting the value of y in second equation

x² - x -42 =13x - 90  

x²- 14x- 42= -90  

x²- 14x+48=0  

x²-6x-8x+48=0

x(x-6)-8(x-6)=0

(x-8)(x-6)=0

x=6 and 8.

To  find the corresponding values for y.  

y=13x-90

y(6)=-12, y(8)=14

Therefore the two solutions are the points:

(6,-12) and (8,14)

To know more about system of equations

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