We have:
The sum of two numbers is 46: x + y = 46
The sum of 6 times the larger and 4 times the smaller is 238: 6x + 4y = 238
Where
x = the larger number
y = the smaller number
Solve the system of equations:
[tex]\begin{gathered} x+y=46 \\ 6x+4y=238 \end{gathered}[/tex]So:
[tex]\begin{gathered} x+y-x=46-x \\ y=46-x \end{gathered}[/tex]Substitute y in the second equation:
[tex]6x+4(46-x)=238[/tex]Simplify and solve for x:
[tex]\begin{gathered} 6x+184-4x=238 \\ 2x+184=238 \\ 2x+184-184=238-184 \\ 2x=54 \\ \frac{2x}{2}=\frac{54}{2} \\ x=27 \end{gathered}[/tex]Then for y:
[tex]y=46-27=19[/tex]Answer:
larger number: 27
smaller number: 19
