Question

use a system of equations with two variables and two equations to solve.A number is 11 more than another number.twice the sum of the two numbers is 42. find the two numbers

Answer 1

"A number is 11 more than another number" can be expressed as

$x=y+11$

"Twice the sum of the two numbers is 42" can be expressed as

$2(x+y)=42$

So, these two equations for a system. Let's combine them to find y in the first place

$\begin{gathered} 2(x+y)=42 \\ 2(y+11+y)=42 \\ 2(2y+11)=42 \\ 2y+11=\frac{42}{2} \\ 2y+11=21 \\ 2y=21-11 \\ 2y=10 \\ y=\frac{10}{2} \\ y=5 \end{gathered}$

Then, we find x

$x=y+11=5+11=16$

The solution is (16, 5).