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
May 21, 2017

Answer:

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 #(-6,-11)#

Explanation:

We solve the set of two equations as simultaneous equations.

Call this Equation 1: #y = 2x+1#
Call this Equation 2: #y = x-5#

Rearrange Equation 2 to make #x# the subject:

#x = y+5#

Substitute this value of #x# into Equation 1:

#y = 2(y+5)+1 = 2y+10+1 =2y+11#

Rearranging:

#-y=11#

#y=-11#

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

#x= -6#

That means the intersection of the lines is at the point #(-6, -11)#.

You could graph the lines to check this solution.

May 21, 2017

Answer:

#(-6,-11)#

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]}