System of equations
• Equation 1
[tex]3x-2y=5[/tex]
• Equation 2
[tex]5x+10y=35[/tex]
Procedure
Solving the system by substitution.
0. Isolating ,x ,from equation 2:
[tex]5x=35-10y[/tex][tex]x=\frac{35}{5}-\frac{10y}{5}[/tex][tex]x=7-2y[/tex]
2. Replacing the expression of x obtained in equation 1:
[tex]3\cdot(7-2y)-2y=5[/tex]
3. Simplifying:
[tex]21-6y-2y=5[/tex][tex]-8y=5-21[/tex][tex]y=\frac{-16}{-8}[/tex][tex]y=2[/tex]
4. Finally, we replace this value in the isolated expression of x and solve it:
[tex]x=7-2\cdot(2)[/tex][tex]x=7-4[/tex][tex]x=3[/tex]
Answer: (3, 2)
