Question

solve the following simultaneous equations by the method of substitutions: 4x+2y=11,3x-5y=-8 ​

Answer 1

Solution

We Have

=> 4x + 2y = 11 .....(i)eq

=> 3x - 5y = -8 .....(ii)eq

Now Take

=> 4x + 2y = 11 .....(i)eq

=> 2y = 11 - 4x

=> y = ( 11 - 4x )/2 .......(iii)eq

Put The value of y on (ii)eq

=> 3x - 5y = -8

=> 3x - 5( 11 - 4x )/2 = - 8

=> 6x - 5(11 - 4x ) = - 16

=> 6x - 55 + 20x = -16

=> 26x = 55 - 16

=> 26x = 39

=> x = 39/26 = 3/2

Now put the value of x on (iii)eq

=> y = ( 11 - 4x )/2 .......(iii)eq

=> y = ( 11 - 4×3/2)/2

=> y = ( 11 - 2 × 3 )/2

=> y = ( 11 - 6)/2

=> y = 5/2

Answer

=> x = 3/2 and y = 5/2

Answer 2

Answer:

Solution=(3/2,5/2)

Step-by-step explanation:

Given:-

4x+2y=11,3x-5y=-8

To find:-

solve the following simultaneous equations by the method of substitutions: 4x+2y=11,3x-5y=-8

Solution:-

Given pair of linear equations are

4x+2y=11------(1)

3x-5y=-8 ------(2)

=>5y=3x+8

=>y=(3x+8)/5----(3)

On substituting the value of y in the equation (1)

=>4x+2[(3x+8)/5]=11

=>4x+[(6x+16)/5]=11

=>[20x+6x+16)/5]=11

=>(26x+16)/5=11

=>26x+16=11×5

=>26x+16=55

=>26x=55-16

=>26x=39

=>x=39/26

=>x=3/2

The value of x=3/2

Substituting the value of x in (3)

=>y=[3(3/2)+8)]/5

=>y=[(9/2)+8]/5

=>y=(9+16)/5

=>y=(25/2)/5

=>y=25/10

=>y=5/2

The value of y=5/2

Answer:-

The solution=(3/2,5/2)

Check:-

x=3/2 and y=5/2 then LHS in equation (1)

=>4(3/2)+2(5/2)

=>6+5

=>11

=>RHS

LHS=RHS

LHS in equation (2) then

=>3(3/2)-5(5/2)

=>(9/2)-(25/2)

=>-16/2

=>-8

=>RHS

LHS=RHS

Verified ✅