Two linear equations by Substitution Method?

1)
4x + 2y = 4
2y = 4 - 4x
y = 2 - 2x

-x + y = 2
-x + (2 - 2x) = 2
2 - 2x - x = 2
-2x - x = 2 - 2
-3x = 0
x = 0/-3
x = 0

4x + 2y = 4
4(0) + 2y = 4
2y = 4
y = 4/2
y = 2

----------------

2)
-x + y = 2
y = 2 + x

x + y = 4
x + (2 + x) = 4
x + x = 4 - 2
2x = 2
x = 2/2
x = 1

-x + y = 2
-1 + y = 2
y = 2 + 1
y = 3

Question 1
y = 4 - 3x
4x + 2(4 - 3x) = 4
4x + 8 - 6x = 4
- 2x = - 4
x = 2

6 + y = 4
y = - 2

x = 2 , y = - 2

Question 2
y = x + 2
x + x + 2 = 4
2x = 2
x = 1

y = 3

x = 1 , y = 3

1} 4x+2y=4
which implies 2y=4-4x
------- y=4-4x/2 [4-4x divided by 2]
=2-2x ---------------------------------Equation 1
3x+y=4
=substitute for y from equation 1.
3x+2-2x=4
x=2
y=2-2[2]
=2-4
y =-2

2] -x+y=2 which implies y=2+x
x+y=4 substitution for y
=x+2+x=4
=2x=2
x=1
y=3

1) Using 2nd equation, y=4-3x.
Substitute that in 1st equation, giving you
4x+2(4-3x)=4 or 4x+8-6x=4 or
-2x=-4 so, x=-4/-2=2.
And just substitute in x-value for either equations,
giving you y=4-(3*2)=4-6=-2,
So, x=2 and y=-2.

4x + 2y = 4 [1]

3x + y = 4 [2]

double the last equation

6x + 2y = 8 [3]

4x + 2y = 4 [1]

take from equation [1]

2x = 4


NB the y's have gone

x = 2

then sub into [1] or [2]

in [2]

6 + y = 4

so y = -2

for second question you do not have to multiply

you can just add the 2 equations together and the x's will cancel

Substitution means replacing something by something else.
a) From (2), we have: y=4-3x.
Replace y by y-3x in (1): 4x + 2(4-3x) = 4
=> 8 - 2x = 4 => x=2 => y=-2

b) From (1): y = 2+x
=> x+ (2+x) = 4 => 2x + 2 =4 => x=1
=> y= 3.