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

We multiply the first equation by -2. This is so that x changes to -2x(Soitwouldmatchthexbelow). We can then crossitover,sincetheequationbelowhas2xand-2x+2x=0.

Answer:23

Step-by-step explanation:x + y = 47

2x + 3y = 100

Solvingstepsx + y = 47 (-2)

2x + 3y = 100

We multiply the first equation by -2. This is so that x changes to -2x(Soitwouldmatchthexbelow). We can thencrossitover,sincetheequationbelowhas2xand-2x+2x=0.-2x – 2y = -94

2x + 3y = 100

Y = 6

Wegety=6bysubtracting-2y(Fromtheaboveequation)from3y.ThisgivesusY.Afterwards,Wesubtract-94(Fromtheaboveequation)from100andthatgivesus6.Therefore,y=6.Togetx.Wesubinthevalueforyintooneoftheequationsandsolve.2x + 3(6) = 100

2x + 18 = 100

Webringover18fromonesidetotheother,togetxalone.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)