Answer:
[tex](\frac{5}{7},\frac{12}{7})[/tex]
Step-by-step explanation:
The given system is
[tex]5x+2y=7[/tex]
[tex]y=x+1[/tex]
We substitute the bottom equation into the top equation to get:
[tex]5x+2(x+1)=7[/tex]
Expand to get:
[tex]5x+2x+2=7[/tex]
Group similar terms:
[tex]5x+2x=7-2[/tex]
Combine similar terms:
[tex]7x=5[/tex]
[tex]x=\frac{5}{7}[/tex]
Put [tex]x=\frac{5}{7}[/tex] into the bottom equation
[tex]y=\frac{5}{7}+1[/tex]
[tex]y=\frac{5+7}{7}[/tex]
[tex]y=\frac{12}{7}[/tex]
The solution is
[tex](\frac{5}{7},\frac{12}{7})[/tex]
