How do you write the the ordered pair that is the solution to the following system of equations: 5x - 2y = 3 and 3x + 4y = 7?

2 Answers
Apr 10, 2017

Answer:

#(1, 1)#

Explanation:

The ordered pair is the set of values of #x# and #y# which can satisfy a given set of algebraic equations and written as #(x, y)# for 2D and as #(x, y, z)# for 3D.

For the set of equations;

#5x - 2y = 3#

#3x + 4y = 7#

We can get the ordered pair by solving them as follows:

Rearranging the 1st equation we have,

#(5x - 3 )/2 = y#

Then, we can substitute this #y# into the 2nd equation,

#=> 3x + 4 *(5x - 3 )/2 = 7#

#=> 3x + 10x - 6 = 7#

#=> 13x = 13#

#=> x = 1#

put the value of #x# back in the 1st equation to get #y#,

#y = (5*1 - 3 )/2#

#=> y = 1#

Therefore, the solution is written in the ordered pair form as

#(x, y ) = (1, 1)#

Apr 10, 2017

Answer:

The solution is #x =1 and y=1#

As an ordered pair it is #(1,1)#

Explanation:

To solve the system of equations you can use several methods.
In this case I would choose elimination of the #y# terms.

#color(white)(..............)5x-2y = 3" "A#
#color(white)(..............)3x+4y=7" "B#

#A xx 2: " "10x-4y =6" "C#
#B+C:" "13x" " = 13#

#color(white)(..................)x=1#

Now that you know the value for #x#, substitute to find a value for #y#

#3(1) +4y =7#
#3+4y=7#
#4y=4#
#y=1#

The solution is #x =1 and y=1#
As an ordered pair it is #(1,1)#