Solve the system by substitution.?

Question

x – 4y = –11
–5x – 3y = –14

Answer 1

Alright, let's start with the first equation:
x - 4y = -11
x = -11 + 4y
Now plug in x for the next equation:
-5(-11 + 4y) - 3y = -14
...distribute:
55 - 20y - 3y = -14
...simplify:
55 - 23y = -14
-23y = - 69
y = 3
Now plug in y into either equation. Let's go ahead and put into the first:
x - 4(3) = -11
x - 12 = -11
x = 1

Answer 2

x – 4y = –11 ..... (1)
–5x – 3y = –14 ..... (2)

(2) * -1,
5x + 3y = 14 (Makes it easier)


Rewrite the two equations.
x – 4y = –11 ...... (1)
5x + 3y = 14 ..... (2)

From (1),
x = 4y - 11

Put x = 4y - 11 in (2)
5(4y - 11) + 3y = 14
20y - 55 + 3y = 14
23y = 69
y = 3

Put y = 3 in (3)
x = 12 - 11
x = 1

x = 1, y = 3 is the solution

Answer 3

x – 4y = –11 add 4y to each side
x=4y-11
–5x – 3y = –14 substitute 4y-11 for x
-5(4y-11)-3y=-14
-20y+55-3y=-14 subtract 55 from each side
-23y=-69 divide both sides by -23
y=3
x=4y-11 substitute 3 for y
x=4*3-11
x=12-11
x=1
(1, 3)

check
-5(1)-3(3)=-14
-5-9=-14
-14=-14

Answer 4

x= -11+4y substitite the value of x in -5x-3y=-14
so, -5(-11+4y)-3y=-14
55-20y-3y=-14
-23y = -69
y = -69/-23
y = 3
substitite y's value in any one of the above equation
x-4y=-11
x-4(3) = -11
x=1

Answer 5

From the first eqn we get
x= -11+4y
Putting the value of x in the second eqn we get,
-5(-11+4y)-3y= -14
=> 55-20y-3y= -14
=>-23y=-14-55= -69
y= -69/-23=3
Putting the value of y in the first eqn
x= -11+4*3=1
x=1 and y=3

Answer 6

x = 4y - 11
-5.(4y - 11) - 3y = - 14
5.(4y - 11) + 3y = 14
20y - 55 + 3y = 14
23y = 69
y = 3
x = 12 - 11
x = 1
SOLUTION is x = 1 , y = 3

Answer 7

x=-11+4y, substitute into 2nd eqn:
-5(-11+4y)-3y=-14;
y=3; x=1

Answer 8

x = 4y - 11
-5(4y-11)-3y=-14
-20y+55-3y=-14
-23y +55=-14
-23y = -69
y=3
x=1

Answer 9

x = 4y - 11

-5(4y - 11) -3y = -14

-23y + 55 = -14

-23y = -69

y = 3

Answer 10

you can also use determinants and matrices to solve these equations once u learn

ax+by=p
cx+dy=q
then
x=
|-11 -4|
|-14 -3| divided by

|1 -4|
|-5 -3|
so x = (33-56)/(-3-20) =-23/-23= 1

y=
|1 -11|
|-5 -14| divided by

|1 -4|
|-5 -3|
so y = (-14-55)/(-3-20) =-69/-23= 3