Respuesta :
[tex]\begin{gathered} 16x+3y=138 \\ 8x+3y=90 \end{gathered}[/tex]
To solve a system of equations you:
1. Solve one of the equations for one of the variables:
Solve x in first variable:
[tex]\begin{gathered} 16x=138-3y \\ \\ x=\frac{138}{16}-\frac{3}{16}y \\ \\ x=\frac{69}{8}-\frac{3}{16}y \end{gathered}[/tex]2. Use the value of x you find in part 1 in the second equation:
[tex]8(\frac{69}{8}-\frac{3}{16}y)+3y=90[/tex]3. Solve for y:
[tex]\begin{gathered} 69-\frac{24}{16}y+3y=90 \\ \\ -\frac{3}{2}y+3y=90-69 \\ \\ \frac{-3y+6y}{2}=21 \\ \\ \frac{3}{2}y=21 \\ \\ y=21(\frac{2}{3})=\frac{42}{3}=14 \end{gathered}[/tex]4. Use the value of y to find the value of x:
[tex]\begin{gathered} x=\frac{69}{8}-\frac{3}{16}y \\ \\ x=\frac{69}{8}-\frac{3}{16}(14) \\ x=\frac{69}{8}-\frac{42}{16} \\ \\ x=\frac{69}{8}-\frac{21}{8}=\frac{48}{8}=6 \end{gathered}[/tex]Then, the solution of the system is ( 6, 14)