Answer:
[tex]x=2, \ y=1[/tex]
Step-by-step explanation:
[tex]\displaystyle \left \{ {{\text{Equation I:} \ \ 2x+y =5} \atop {\text{ Equation II:} \ \ 3x-2y=4}} \right.[/tex]
Multiply [tex]\text{Equation I}[/tex] by 2.
- [tex]2 \ \Big{[}2x+y=5\Big{]}[/tex]
- [tex]4x+2y=10[/tex]
Now we have this system of equations:
- [tex]\displaystyle \left \{ {{4x+2y =10} \atop {3x-2y=4}} \right.[/tex]
We can add the equations together to cancel out y.
- [tex]7x=14[/tex]
- [tex]x=2[/tex]
Substitute x = 2 into the first equation and solve for y.
- [tex]2(2)+y=5[/tex]
- [tex]4+y=5[/tex]
- [tex]y=1[/tex]
The solution to this system of equations is:
- [tex]x=2, \ y=1[/tex]
- or [tex](2, \ 1)[/tex]
