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