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Answer:
Kendall's age 6 years ago was 23 years.
Step-by-step explanation:
A system of equations is a set of equations with the same unknowns. A system of linear equations is a system of equations in which each equation is linear. That is, a system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
In this case you propose a system, being the variables to solve:
6 years ago, Kelly was younger than Kendall by 6 years. The total age of Kelly and Kendall now is 52 years. So, the system of equations is:
[tex]\left \{ {{x=y-6} \atop {(x+6)+(y+6)=52}} \right.[/tex]
It is solved by the substitution method, which consists of solving one of the unknowns in one of the equations and substituting its value in the following one. The first equation is replaced in the second equation of the system:
(y-6+6)+(y+6)=52
y +(y+6)= 52
y +y+6= 52
2*y + 6=52
2*y= 46
y= 46 ÷ 2
y=23
So, Kendall's age 6 years ago was 23 years.