Solve using the substitution method???

Question

These are two problems.

1) x+y=6
x-y=4


2) 3x+4y=20
3x-2y=8

Answer 1

Solve for Y on the bottom one, circle it and draw an arrow to the Y on the top one. Then substitute it where there was a Y. You now only have to solve for one variable just combine like terms and solve for X. You've now found both X & Y

Answer 2

You need to get a variable (letter) on one side by itself.
So in problem 1. you have x + y = 6. So subtract y from both sides and you get x = (6-y) Now plug that value in to the second equation.
x- y = 4 becomes (6-y)-y = 4. Or 6-2y = 4
Subtract 6 from both sides.
-2y = -2
Divide both sides by -2 and you get y = 1.
Since you know that x = (6-y) you substitute the 1 for y.
x = 6-1 or 5. So x is 5 and y is 1.

For problem 2.
3x + 4y = 20 Subtract 4y
3x = 20 - 4y Divide by 3.
x = (20 - 4y)/3

Plug into equation 2. 3x -2y = 8 becomes
3(20-4y)/3 -2y = 8 or (20-4y) -2y = 8 or 20 - 6y =8
Subtract 20
-6y = 8-20 or -12 Divide by -6
y = 2 Since x = (20 -4y)/3 = (20 -8)/3 = 12/3 =4
y is 2 and x is 4.

Answer 3

1. First equation gives y = 6-x, substitute into second:
x - (6-x) = 4
=> x - 6 + x = 4
=> 2x = 10
=> x = 5
y = 6-x = 1.
So x = 5 and y = 1.

2. Second equation gives 2y = 3x - 8, substitute into first equation:
3x + 2(3x - 8) = 20
=> 3x + 6x - 16 = 20
=> 9x = 36
=> x = 4
2y = 12 - 8 = 4 => y = 2.
So x = 4 and y = 2.

Answer 4

1) x-y = 4 => x = y+4
sub in y+4 for x in the first equation
(y+4) + y = 6
2y= 2
y =1
plug in y = 1 into either equations
x +1 = 6
x = 5
y = 1

2) as you see there is the term "3x" in both equations so solve for that in one of them
3x - 2y = 8 => 3x = 2y + 8
sub in 2y + 8 into the first equation for 3x
(2y + 8) +4y = 20
6y = 12
y = 2
plug y = 2 into either equation
3x + 8 = 20
3x = 12
x = 4
y = 2

Answer 5

x+y=6 -------->1
x-y=4 --------->2

add 1&2
=>x+y+x-y=6+4
=>2x=10
=>x=5
substitute x=5 in any of above equations
x+y=6
=>5+y=6
=>y=1
therefore solutions are x=5,y=1


3x+4y=20 -------->1
3x-2y=8 --------->2

sub 2 from 1
=>3x+4y-3x+2y=20-8
=>6y=12
=>y=2
substitute y=2 in any of above equations
3x+4y=20
=>3x+8=20
=>x=4
therefore solutions are x=4,y=2

Answer 6

x+y= 6
x=6-y

x-y=4
substitute what you found for x above
(6-y) - y = 4
6-2y = 4
-2y = -2
y=1*
plug into one of the original equations
x+ (1) = 6
x = 5*



#2

3x+4y=20
3x-2y = 8

3x = 8+2y
(8+2y) + 4y = 20
8+ 6y = 20
6y = 12
y = 2*
plug into original...
3x - 2(2) = 8
3x-4=8
3x=12
x=4*