Verify whether the ordered pair (5, -2) is a solution to the system. 2x -3y = 164x + 6y = 8

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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To verify if the point (5, -2) is a solution to the system, then the point (5,-2) must verify both equations:

Let us check:

2x-3y=16

2(5)-3(-2)=16

10 + 6= 16

16=16

Then, the point (5, -2) verifies the first equation.

Now let us check the second equation:

4x+6y=8

4(5)+6(-2)=8

20 -12 =8

8=8

Then the point (5,-2) is a solution to the system.

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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2x -  3y = 16
4x + 6y = 8

To check if (5, -2) is solution to this system, all you have to do is to plug it in

First, let's check the first equation

2 ( 5 ) - 3 ( -2 ) = 16 multiply 5 with 2 and -3 with -2

By multiplying, your equation should look like

10 + 6 = 16 add 10 with 6

By adding, your should get

16 = 16 which means (5, -2 ) goes into this equation

Now, let's check the second equation

4 ( 5 ) + 6 ( -2 ) = 8 multiply 4 with 5 and 6 with -2

By multiplying, you should get

20 - 12 = 8 now subtract 20 with 12

By subtracting, your should get

8 = 8 which means ( 5, -2 ) goes into this equation as well

Since ( 5, -2 ) is able to go into both of the equation and still make it true, that means ( 5, -2 ) is a solution to this system

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To prove that the pair  (5, -2) is the solution of the system, you just have to substitute x and y from the equations of the system, by the values 5 and -2.

Let's see:

2*5 -3*(-2) = 16 => 10 + 6 = 16 => 16 = 16
4*5 + 6*(-2) = 8 => 20 - 12 = 8 => 8 = 8

Since both equation are verified by the values from the given pair, that means that the pair (5,-2) represents the solution of the system.

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

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Ordered pair (5, -2) means

x = 5 and y = -2

The simplest way to verify if this ordered pair is solution to the system of two given simultaneous equation is to substitute the values of x and y in the equation and see if the equations holds true.

The two simultaneous equations are:

2x - 3y = 16   ...   (1)

4x + 6y = 8   ...   (2)

Substituting value of x an y in equation (1) we get:

4*5 + 6*(-2) = 8

20 - 12 = 8

8 = 8

Thus the equation (1) holds true for given pair of values for x and y.

Similarly substituting value of x an y in equation (2) we get:

2*5 - 3*(-2) = 16

10 + 6 = 16

16 = 16

Thus the equation (2) holds true for given pair of values for x and y.

Therefore the given ordered pair is a solution to the system of given simultaneous equations.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

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To verify whether the ordered pair is a solution pf the system

2x+3y =16 ........(1) and

4x+3y ==8.........(2)

Verification:

Put x=5 and y =-2 in the first and 2nd equations :

LHS 2(5)-3(-2) = 10+6 = 16 = RHS. So first equation is satisfied b(5,-2)

2nd equation:

LHS: 4(5)+6(-2) =20-12 =8 = RHS. 2nd equation is satisfied by(5,-2).

 

 

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