Answer:
18 and 40
Step-by-step explanation:
Let x be the age of Claire and y the age of her mother
Claire's mother is 4 years more than twice Claire's age
The sum of their ages are is 58
the system is:
[tex]\left \{ {{y=2x-4} \atop {y+x=58}} \right.[/tex]
Multiply (y+x = 58) by -1 and then add it to (y = 2x+4) to eliminate y
- -y-x = -58
- -y-x+y = 2x+4-58
- -x -2x = -54
- -3x = -54
- x = 54/3
- x = 18
y= 58-18 = 40
so claire's mother is 40 years old and claire is 18
