Question

Solve the system of equations and choose the correct ordered pair.
5x+2y= 19
4x-3y = 6

Answer 1

The solution of given system of equation is (3,2).

Explanation:

The given system of equations is

`5x+2y=19` .... (1)

`4x-3y=6` .... (2)

Solve the system of equations using elimination method.

Multiply equation (1) by 3 and multiply equation (2) by 2.

`15x+6y=57` .... (3)

`8x-6y=12` .... (4)

Now, add the equations (3) and (4), to eliminate y.

`15x+8x=57+12`

`23x=69`

Divide both sides by 23.

`x=3`

The value of x is 3. Substitute x=3 in equation (1), to find the value of y.

`5(3)+2y=19`

`15+2y=19`

Subtract 15 from both the sides.

`2y=19-15`

`2y=4`

Divide both sides by 2.

`y=2`

The value of y is 2.

Therefore the solution of given system of equation is (3,2).

Answer 2

(3, 2)

Explanation:

First, we have to eliminate a variable:

3(5x+2y = 19 )

2(4x-3y = 6)

------------------

15x+6y = 57

8x-6y = 12

Now we add the system of equations together:

15x+8x+6y-6y = 57+12

23x = 69

/23 /23

x = 3

Now we can plug this value back into one of the equations to get y:

5(3)+2y = 19

15+2y = 19

-15 -15

2y = 4

/2 /2

y = 2

Therefore, the solution to these system of equations is (3, 2)