# How do you write the the ordered pair that is the solution to the following system of equations: #y= 2x + 1# and #y = x -5#?

##### 2 Answers

The ordered pair will simply be the point at which these two lines cross. We solve the equations as simultaneous equations.

The solution is the point

#### Explanation:

We solve the set of two equations as simultaneous equations.

Call this Equation 1:

Call this Equation 2:

Rearrange Equation 2 to make

Substitute this value of

Rearranging:

We can substitute this into either equation to find the value of

That means the intersection of the lines is at the point

You could graph the lines to check this solution.

#### Explanation:

#"solve the equations using the method of "color(blue)"substitution"#

#color(red)(y)=2x+1to(1)#

#color(red)(y)=x-5to(2)#

#"since both equations express y in terms of x, we can"#

#"equate the right sides"#

#rArr2x+1=x-5#

#"subtract x from both sides"#

#2x-x+1=cancel(x)cancel(-x)-5#

#rArrx+1=-5#

#"subtract 1 from both sides"#

#xcancel(+1)cancel(-1)=-5-1#

#rArrx=-6#

#"substitute this value into either " (1)" or " (2)#

#"substituting in " (2)" and evaluating for y gives"#

#y=-6-5=-11#

#rArr" point of intersection "=(-6,-11)#

graph{(y-2x-1)(y-x+5)=0 [-40.54, 40.54, -20.28, 20.26]}