# Use the substitution method to solve this system of equations -3x + y = 11 ...

Use the substitution method to solve this system of equations

-3x + y = 11

5x - 2y = -16

Enter answer as an ordered pair using ( )

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Solve the system by using substitution.

`i. )-3x + y = 11`

`ii.) 5x - 2y = -16`

First solve equation i. for y.

`-3x + y = 11`

`y = 3x + 11`

Now substitute the value of y, (3x + 11), for y in the second equation.

`5x - 2y = -16`

`5x - 2(3x + 11) = -16` Solve for x.

`5x - 6x - 22 = -16`

`-x -22 = -16`

`-x = 6` or `x = -6`

Now substitute the value of x, -6, into either of the original equations to find y.

`-3x + y = 11`

` ` `-3(-6) + y = 11`

`18 + y = 11`

`y = -7`

**The solution to the system using substitution is (-6, -7).**

The system of equations -3x + y = 11 and 5x - 2y = -16 has to be solved for x and y.

From -3x + y = 11, x = (y - 11)/3

Substitute this in 5x - 2y = -16

(5*(y - 11))/3 - 2y = -16

5y - 55 - 6y = -48

-y = 7

y = -7

Substitute y = -7 in x = (y - 11)/3

x = (-7 - 11)/3 = -6

The solution of the system of equations is x = -6 and y = -7

`-3x + y = 11` .................(i)

`5x - 2y = -16` ..................(ii)

From equation (i) we get:

`y=11+3x` ..............(iii)

Now, substituting the value of y in equation (ii) we get:

`5x-2(11+3x)=-16`

`rArr 5x-22-6x=-16`

`rArr -x-22=-16`

`rArr x+22=16`

`rArr x=16-22`

`rArr x=-6`

Putting the value of x in equation (iii) we get:

`y=11+3*(-6)=11-18=-7`

**Therefore, by substitution method, the solution for the given system of equations is (-6,-7)**.

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Check:

(i) `-3*(-6)+(-7)=18-7=11`

(ii) `5*(-6)-2*(-7)=-30+14=-16`