Solve the system of equations using the substitution method.?

y=1+3x

5x+ 2(1+3x)= -4

11x= -7

x= -7/11

y= -21/11+1

y= -10/11

Solve one equation for x or y, then substitute that value into the other equation:

-3x + y = 1

y = 3x + 1

Now plug in that "y" into the other equation:

5x + 2y = -4

5x + 2(3x + 1) = -4

5x + 6x + 2 = -4

11x = -6

x = -6/11

Now plug that back into either eqation and solve for y:

y = 3x + 1

y = 3(-6/11) + 1

y = -18/11 + 11/11

y = -7/11

(-6/11, -7/11)

checking:

5x + 2y = -4

5(-6/11) + 2(-7/11) = -4

-30/11 -14/11 = -4

-44/11 = -4

-4 = -4

TRUE!

well, the first equation is -3x+y=1, you could rewrite that as y=3x+1

so, substitute that into the second equation

5x+2(3x+1)=-4

5x+6x+2=-4

11x=-6

x=-6/11

so, plug that in to the first equation (or the second)

-3(-6/11)+Y=1

18/11+y=1

y=-7/11

so x = -6/11 and y = -7/11

check your answers by inserting them into the equations

y = 3x + 1

5x + 2(3x + 1) = - 4

5x + 6x + 2 = - 4

11x = - 6

x = - 6/11

y = - 18/11 + 1

y = - 7/11

x = - 6/11 , y = - 7/11

if you want to know how to use substitution just isolate the variable to one side then insert it where the isolated variable in the first pair is Ex: -3x+y=1

y= 3x + 1 insert this into the other equation

5x+2(3x+1)=-4

3x + y = 7 4x - y = 21 3x + y = 7 y = 7 - 3x 4x - y = 21 4x - (7 - 3x) = 21 4x - 7 + 3x = 21 4x + 3x = 21 + 7 7x = 28 x = 28/7 x = 4 4x - y = 21 4(4) - y = 21 -y = 21 - 16 -y = 5 y = 5/-1 y = -5 ∴ x = 4 , y = -5 (4,-5)

-3x+y=1

5x+2y=-4

y=3x+1

5x+2(3x+1)=-4

5x+6x+2=-4

11x=-6

x=-6/11

-3/1(-6/11)+y=1

-18/11+y=1

y=-7/11