Question

2x+3y=9 and 4x-6y=18 solve using substitution methad

Answer 1

Given: 2x+3y=9

           4x-6y=18

To Find: solve these equations by using substitution method.

Solution:

In substitution method, we solve one equation for one of the variables and substitute that value in other equation. after this step, there will be one equation only with one variable, which can be easily solved.

Step 1:

           2x+3y=9 ..............(eqn 1)

           4x-6y=18  ............(eqn 2)

divide equation 2 by 2 on both sides, we get:

           2x - 3y = 9

           2x = 9 + 3y

             x = (9+ 3y)/2   ..........(eqn 3)

step 2:

now put the value of x (from equation 3) in equation 1, we get:

            2((9+ 3y)/2) + 3y = 9

             (9 + 3y) +3y = 9

              9 + 6y =9

              6y = 9-9

              6y = 0

                y = 0   .........................(eqn 4)

step 3:

Now put the value of y = 0 (from equation 4) in equation 3, we get

           x = (9+ 3(0))/2

           x = 9/2

           x = 4.5  .......................(eqn 5)

so the answer is  x = 4.5 and y = 0.

step 4:

Verification:

to verify the answer we can put these values of x and y in any one of the equation 1 or equation 2.

put  x = 4.5 and y = 0  in equation 1, we get

             2x+3y=9

             2(4.5) + 3(0) = 9

              9 + 0 = 9

                9 = 9

            L.H.S. = R.H.S.

It means our answer is right.

           

Answer 2

Step-by-step explanation:

Given that: 2x+3y=9 and 4x-6y=18

To find: Solution of equations using substitution method

Solution:

In this method find value of one variable from one equation and place to other

$2x + 3y = 9 \: \: ...eq1 \\ \\ 3y = 9 - 2x \: \: \: ...eq2 \\ \\ 4x - 6y = 18 \: \: \: eq3$

Value of y from eq 2 placed in eq3

$4x - 2(3y) = 18 \\ \\ 4x - 2(9 - 2x) = 18 \\ \\ 4x + 4x - 18 = 18 \\ \\ 8x = 36 \\ \\ x = \frac{36}{8} \\ \\ \bold{x = \frac{9}{2} }$

Now place the value of x in eq1

$2x + 3y = 9 \\ \\ 2 \times \frac{9}{2} + 3y = 9 \\ \\ 3y = 9 - 9 \\ \\ 3y = 0 \\ \\ \bold{y = 0}$

Thus,

$\bold{x = \frac{9}{2}=4.5,\:\: y = 0}$

is the solution of given equations.

Hope it helps you.