Step-by-step explanation:
x = 6, y = -2
Step-by-step explanation:
Let the numbers be x and y.
x + 2y = 2
x = 2 - 2y --(1)
2x + y = 10 --(2)
sub (1) into (2):
2(2 - 2y) + y = 10
4 - 3y = 10
y = -2
when y = -2, x = 6
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6 and 2
Step-by-step explanation:
Let the first number =a
Let the second number =b
A first number plus twice a second number is 14.
a+2b=14Twice the first number plus the second totals 10.
2a+b=10We solve the two equations simultaneously
Recall:
a=14-2b
=14-2(6)
=14-12
a=2
The two numbers are 6 and 2.
1. This is a like term
24 = 24
2. This is not a like term
12x - 6 = 46
3. This is not a like term
33 = 5x + 43
4.This is a like term
1 = 1
5. This is not a like term
7x = -48
6. This is a like term
25 = 25
7. This is a like term
60 = 60
8. This is a like term
47 = 47
9.This is a like term
20.6 = 20.6
10.This is a like term
10 = 10
Step-by-step explanation:
1. 5x + 4x − 6x = 24
5x + 4x = 9x
9x - 6x = 24
3x = 24
We can replace x and turn it into an 8.
3(8) = 24
3 x 8 = 24
24 = 24
This is a like term.
2. 8x + 5 − 4x + 1 = 46
8x + 4x - 5 + 1 = 46
8x + 4x = 12x
12x - 5 + 1 = 46
5 + 1 = 6
12x - 6 = 46
We cannot replace the x with any number to get 46.
So this is not a like term.
3. 33 = 5(x + 8) + 3
5xX= 5x
5 x 8 = 40
33 = 5x + 40 + 3
40 + 3 = 43
33 = 5x + 43
We cannot replace any number with x and get 33.
This is not a like term.
4. 2x + 3(x − 8) = 1
3 x X = 3x
3 x 8 = 24
2x + 3x - 24 = 1
2x + 3x = 5x
5x - 24 = 1
We can replace the x with 5.
5(5) - 24 = 1
5 x 5 = 25
25 - 24 = 1
1 = 1
This is a like term
5. x + x − 2x + 4x = −48
x + x = 1x because x is always a 1
1x - 2x +4x = -48
1x + 2x = 3x
4x + 3x = 7x
7x = -48
We cannot replace x with any number.
This is not a like term.
6. 2(x + 5) + 3x = 25
2 x X = 2x
2 x 5 = 10
2x + 10 + 3x = 25
2x + 3x + 10 = 25
2x + 3x = 5x
5x + 10 = 25
We can replace the x with a 3.
5(3) + 10 = 25
5 x 3 = 15
15 + 10 = 25
25 = 25
This is a like term.
7. 60 = 4(x + 3) + 2(x − 3)
4 x X = 4x
4 x 3 = 12
60 = 4x + 12 + 2(x - 3)
2 x X = 2x
2 x 3 = 6
60 = 4x + 12 + 2x - 6
60 = 4x +2x +12 - 6
4x - 2x = 2x
60 = 2x + 12 - 6
12 - 6 = 6
60 = 2x + 6
We can replace the x with a 33.
60 = 2(33) - 6
2 x 33 = 66
66 - 6 = 60
60 = 60
This is a like term.
8. 47 = 2(x + 3) + 3(x − 3)
2 x X = 2x
2 x 3 = 6
47 = 2x + 6 + 3(x - 3)
3 x X = 3x
3 x 3 = 9
47 = 2x + 6 + 3x - 9
47 = 2x + 3x + 6 - 9
2x + 3x = 5x
47 = 5x + 6 - 9
6 - 9 = -3
47 = 5x + -3
We can replace the x with a 10.
47 = 5(10) + -3
5 x 10 = 50
47 = 50 + -3
50 + -3 = 47
47 = 47
This is a like term.
9. −2(x + 1.4) − 1.8 = 20.6
-2 x X = -2x
-2 x 1.4 = -2.8
-2x + -2.8 - 1.8 = 20.6
-2.8 - 1.8 = -4.6
-2x + -4.6 = 20.6
We can replace x with a 8.
-2(8) + -4.6 = 20.6
-2 x 8 = -16
-16 + -4.6 = 20.6
20.6 = 20.6
This is a like term.
10. 8 − 2(x + 4) = 10
2 x X = 2x
2 x 4 = 8
8 - 2x + 8 = 10
8 - 8 + 2x = 10
8 - 8 = 0
0 + 2x = 10
We can replace x with 5.
0 + 2(5) = 10
2 x 5 = 10
0 + 10 = 10
10 = 10
This is a like term.
I hope this helped. I am sorry if you get this wrong. Have a wonderful day.
1. This is a like term
24 = 24
2. This is not a like term
12x - 6 = 46
3. This is not a like term
33 = 5x + 43
4.This is a like term
1 = 1
5. This is not a like term
7x = -48
6. This is a like term
25 = 25
7. This is a like term
60 = 60
8. This is a like term
47 = 47
9.This is a like term
20.6 = 20.6
10.This is a like term
10 = 10
Step-by-step explanation:
1. 5x + 4x − 6x = 24
5x + 4x = 9x
9x - 6x = 24
3x = 24
We can replace x and turn it into an 8.
3(8) = 24
3 x 8 = 24
24 = 24
This is a like term.
2. 8x + 5 − 4x + 1 = 46
8x + 4x - 5 + 1 = 46
8x + 4x = 12x
12x - 5 + 1 = 46
5 + 1 = 6
12x - 6 = 46
We cannot replace the x with any number to get 46.
So this is not a like term.
3. 33 = 5(x + 8) + 3
5xX= 5x
5 x 8 = 40
33 = 5x + 40 + 3
40 + 3 = 43
33 = 5x + 43
We cannot replace any number with x and get 33.
This is not a like term.
4. 2x + 3(x − 8) = 1
3 x X = 3x
3 x 8 = 24
2x + 3x - 24 = 1
2x + 3x = 5x
5x - 24 = 1
We can replace the x with 5.
5(5) - 24 = 1
5 x 5 = 25
25 - 24 = 1
1 = 1
This is a like term
5. x + x − 2x + 4x = −48
x + x = 1x because x is always a 1
1x - 2x +4x = -48
1x + 2x = 3x
4x + 3x = 7x
7x = -48
We cannot replace x with any number.
This is not a like term.
6. 2(x + 5) + 3x = 25
2 x X = 2x
2 x 5 = 10
2x + 10 + 3x = 25
2x + 3x + 10 = 25
2x + 3x = 5x
5x + 10 = 25
We can replace the x with a 3.
5(3) + 10 = 25
5 x 3 = 15
15 + 10 = 25
25 = 25
This is a like term.
7. 60 = 4(x + 3) + 2(x − 3)
4 x X = 4x
4 x 3 = 12
60 = 4x + 12 + 2(x - 3)
2 x X = 2x
2 x 3 = 6
60 = 4x + 12 + 2x - 6
60 = 4x +2x +12 - 6
4x - 2x = 2x
60 = 2x + 12 - 6
12 - 6 = 6
60 = 2x + 6
We can replace the x with a 33.
60 = 2(33) - 6
2 x 33 = 66
66 - 6 = 60
60 = 60
This is a like term.
8. 47 = 2(x + 3) + 3(x − 3)
2 x X = 2x
2 x 3 = 6
47 = 2x + 6 + 3(x - 3)
3 x X = 3x
3 x 3 = 9
47 = 2x + 6 + 3x - 9
47 = 2x + 3x + 6 - 9
2x + 3x = 5x
47 = 5x + 6 - 9
6 - 9 = -3
47 = 5x + -3
We can replace the x with a 10.
47 = 5(10) + -3
5 x 10 = 50
47 = 50 + -3
50 + -3 = 47
47 = 47
This is a like term.
9. −2(x + 1.4) − 1.8 = 20.6
-2 x X = -2x
-2 x 1.4 = -2.8
-2x + -2.8 - 1.8 = 20.6
-2.8 - 1.8 = -4.6
-2x + -4.6 = 20.6
We can replace x with a 8.
-2(8) + -4.6 = 20.6
-2 x 8 = -16
-16 + -4.6 = 20.6
20.6 = 20.6
This is a like term.
10. 8 − 2(x + 4) = 10
2 x X = 2x
2 x 4 = 8
8 - 2x + 8 = 10
8 - 8 + 2x = 10
8 - 8 = 0
0 + 2x = 10
We can replace x with 5.
0 + 2(5) = 10
2 x 5 = 10
0 + 10 = 10
10 = 10
This is a like term.
I hope this helped. I am sorry if you get this wrong. Have a wonderful day.
The numbers are
Step-by-step explanation:
Step(i):-
Given sum of the three numbers is 10
Let x , y , z be the three numbers is 10
x +y + z = 10 ...(i)
Given two times the second number minus the first number is equal to 12
2 × y - x = 12 ...(ii)
Given the first number minus the second number plus twice the third number equals 7
x + y + 2 z = 7 ...(iii)
Step(ii):-
Solving (i) and (iii) equations
x + y + z = 10 ...(i)
x + y + 2 z = 7 .. (iii)
- - - -
0 0 -z = 3
Now we know that z = -3 ...(a)
from (ii) equation
2 × y - x = 12 ...(ii)
x = 2 y -12 ...(b)
Step(iii):-
substitute equations (a) and (b) in equation (i)
x+y+z =10
2 y - 12 + y -3 =10
3 y -15 =10
3 y = 10 +15
3 y =25
Substitute and z = -3 in equation(i) we will get
x+y+z =10
Final answer :-
The numbers are
Step-by-step explanation:
The answer to your question is x = -2, y = 5 and z = 7
Step-by-step explanation:
Data
first number = x
second number = y
third number = z
Process
1.- Write equations to solve this problem
x + y + z = 10 Equation l
2y - x = 12 Equation ll
x - y + 2z = 7 Equation lll
2.- Solve equation ll for x
x = 2y - 12
3.- Substitute the previous equation in equation l and lll
(2y - 12) + y + z = 10 (2y - 12) - y + 2z = 7
2y - 12 + y + z = 10 2y - 12 - y + 2z = 7
3y + z = 10 + 12 y + 2z = 19
3y + z = 22
4.- Solve for y and z
-2(3y + z = 22)
y + 2z = 19
-6y - 2z = -44
y + 2z = 19
-5y + 0 = -25
y = -25/-5
y = 5
-Find z
5 + 2z = 19
2z = 19 - 5
2z = 14
z = 14/2
z = 7
5.- Find x
x + 5 + 7 = 10
x = 10 - 5 - 7
x = -2
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