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

(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

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)