Answer:
a= 5 and b=1
Step-by-step explanation:
To solve, we will follow the steps below:
2x + 3y = 7
(a-b)x + (a+b)y = 3a + b - 2
We should note that since it has infinitely many solutions then,
Hence
2/a-b = 3/a+b = 7/3a +b-2
2/a-b = 3/a+b
cross-multiply
3(a-b) = 2( a+b)
open the bracket
3a - 3b = 2a + 2b
collect like term
3a - 2a = 2b + 3b
a = 5b -------------------------------------------(1)
Similarly
3/a+b = 7/3a +b-2
cross-multiply
7(a+b) = 3(3a+b -2)
7a + 7b = 9a + 3b -6
take all the variables to the left-hand side of the equation
7a - 9a+ 7b-3b = -6
-2a + 4b = -6 ---------------------------------(2)
but a = 5b
substitute a= 5b in equation (2) and solve for b
-2(5) + 4b = -6
-10 + 4b = -6
add 10 to both-side of the equation
-10 + 10+ 4b = -6+10
4b = 4
divide both-side of the equation by 4
b = 1
substitute b= 1 in equation (1)
a = 5b
a =5(1)
a=5
Therefore, a= 5 and b=1
Answer:
$5.10
Step-by-step explanation:
The owner buys 5 panes of glass for $12.75. So to find the cost of 1, we need to divide the total cost by the amount of planes. In this case, 12.75 divided by 5. This gives you $2.55 per plane. And since he is buying 2 more, we would multiply the cost of the plane (2.55) by the amount we are buying (2). So we do 2.55 X 2 and we get $5.10
Answer:
Step-by-step explanation:
Let h be the number of hats Elliott makes and s be the number of scarves she makes.
Each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats. This is expressed as
h = 2s
The total number of hats and scarves that she wants to make is 20. This is expressed as
h + s = 20
Therefore, the system of equations that represents this situation are
h = 2s
h + s = 20
Answer:
You should probably be more specific as different schools have different curriculum's!
Step-by-step explanation:
Answer:
5y-2xy
6q-6
Step-by-step explanation:
For the first expression, we can multiply 5 by y to get 5y. Thats all we can simplify it though, because xy is not equal to x or y.
For the second equation, we can easily add the variables to simplify. 6q-6
Hope this helps!
