Solve by substitution method:?

Question

Solve by substitution method:
5x - 6y = 21
x - 2y = 5

Answer 1

from 2nd equ
x=2y+5

5x-6y=21
5(2y+5)-6y=21
4y=-4
y=-1

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

Answer 2

5x - 6y = 21..... Eq 1
x - 2y = 5..... Eq 2
Consider Eq 2
x - 2y = 5
-2y = 5 - x
2y = -(5 - x)
2y = x - 5
y = (x - 5)/2
Substitute the derived value of 'y' in Eq 1
5x - 6y = 21
5x - 6[(x - 5)/2)] = 21
5x - 3(x - 5) = 21
5x - 3x + 15 = 21
2x = 21 - 15
2x = 6
x = 6/2
x = 3
Substitute the value of 'x' in Eq 2
x - 2y = 5
3 - 2y = 5
-2y = 5 -3
-2y = 2
y = 2/-2
y = -1

Answer 3

5x - 6y = 21
x - 2y = 5
from second eq
x=5+2y
plug in first eq
5(5+2y)-2y=5
25+10y-2y=5
8y=-20
y=-5/2
so x=5+2(-5/2)
=0

Answer 4

Substitue 4y-2 or 6y+8 into between the equations, whichever one you choose for would be high quality because of the fact this is going to be an identical equation no remember what, only backwards. i'm going to objective to simplify it greater: eq. a million) x=4y-2 eq. 2) x=6y+8 replace the two 4y-2 or 6y+8 into the different equation. in case you employ 4y-2 from eq. a million, eq. 2 could now look like this: 4y-2=6y+8 because of the fact if x is 4y-2, you may only placed it precise into the place the x is in eq. 2 - because of the fact x IS 4y-2. this is an identical for in case you employ 6y+8 from eq. 2 -- x IS 6y+8 so which you would be able to placed this word into equation one the place the x is as a results of the fact 6y+8 equals x. it may look like this - 6y+8=4y-2 Then when you have the two 6y+8=4y-2 or 4y-2=6y+8, you may resolve for y with the help of including jointly like words. using 4y-2=6y+8...... upload the 4y and 6y jointly with the help of subtracting 4y from the helpful 4y on the left edge of the equivalent sign and with the help of 6y to get 2y on the the superb option edge of the equivalent sign : 4y-2=6y+8 -4y -4y ^ the +4y and -4y cancels out leaving... -2=2y+8 you attempt to get y with the help of itself, so which you would be able to desire to subtract 8 from the helpful 8 on the the superb option part and subtract 8 from the adverse 2 on the left to get -10 on the left: -2=2y+8 -8 -8 ^ the +8 and - 8 cancels out leaving.... -10=2y To get y with the help of itself, you may desire to divide the 2y with the help of two (do the choice to cancel the two out, like we did while it turn into addition/subtraction), and divide the -10 with the help of two: -10=2y -10/2=2y/2 ^the better 2 and divided 2 cancels out leaving.... -5=y <--- -5 IS y ---- So now which you have y, you may put in -5 in the two eq.a million or 2 and resolve : (using eq a million): x = 4y-2 x = 4(-5)-2 x = -20-2 x = -22 ! So the ordered pair to unravel those equations is (x, y) : (-22, -5)

Answer 5

x=5+2y

5(5+2y)-6y=21
25+10y-6y=21
4y=-4
y=-1

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