Substitution Method?

Question

Use the substitution method to solve the linear system.

4) -4x+7y= -2
x= -y-5



5) 7x+ 4y=5
x-6y= -19




If you can please help me out with both, that will be GREAT, if not, please help me out with atleast one! Thank You!

Answer 1

4. -4(-y-5)+7y=2

5. don't know about this one

Answer 2

(4) - 4x+7y= -2 (eqn.no. 1) and x= -y-5 (eqn.no.2) Substituting the value of x in eqn.no.1,we get -4( -y-5) +7y = -2 => 4y+20+7y= -2 => 11y = -2 -20 = -22 => y= -22/11= -2 putting the value of y in eqn.no 2 we get, x=2-5= -3 (5)7x +4y=5 (eqn. no. 1) and x -6y= -19 or x= 6y-19 (eqn. no.2 ) Substituting the value of x in eqn. no. (1) ,we get 7(6y-19) +4y= 5 => 42y - 133 +4y =5 => 46y= 5+133= 138 => y= 138/46=3 Putting the value of y in eqn. no (1).we get x=6*3 - 19=18- 19= -1

Answer 3

Substitution is replacing one thing with its equivalent even if it's in a different form. You can either substiture x or y into one equation. You have two equations in each problem so you need to pick one to put in the other. Usually you'd start with the simpler one, find what x is equal to or what y is equal to depending on if you want to put X or Y in the other equation. Example:
x=2y
7x + 3y = 5

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x = 2y is really simple so I'll put it wherever there's an x in the second equation.
so you have
7*(2y) + 3y = 5
Now all that's left is multiplying out and simplifying.

Good luck

Answer 4

#4) -4x+7y=-2
-4(-y-5) + 7y= -2
4y+20+7y= -2
20+11y=-2
11y=-22
y=-2

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


#5)
x-6y=-19
x= -19+6y
than
7(-19+6y)+4y=5
-133 + 42y +4y=5
-133 + 46y= 5
46y=138
y=3
making 7x+4(3) = 5
7X+12=5
7X= -7
x=-1