The sum of two numbers is 47. twice the first number and three times the second number have a sum of 100. Set up a system of equations to find the numbers
Question
Question
The sum of two numbers is 47. twice the first number and three times the second number have a sum of 100. Set up a system of equations to find the numbers
Answer:
23
Step-by-step explanation:
x + y = 47
2x + 3y = 100
Solving steps
x + y = 47 (-2)
2x + 3y = 100
We multiply the first equation by -2. This is so that x changes to -2x (So it would match the x below). We can then cross it over, since the equation below has 2x and -2x + 2x = 0.
-2x – 2y = -94
2x + 3y = 100
Y = 6
We get y = 6 by subtracting -2y (From the above equation) from 3y. This gives us Y. Afterwards, We subtract -94 (From the above equation) from 100 and that gives us 6. Therefore, y = 6.
To get x. We sub in the value for y into one of the equations and solve.
2x + 3(6) = 100
2x + 18 = 100
We bring over 18 from one side to the other, to get x alone. We have to change 18 to – 18 because it crosses over to the other side.
2x = 100 – 18
2x = 72
x = 72÷2
x = 36.
X = 36
Y = 6
(36, 6)