Answer:
One solution (6, 7)
Step-by-step explanation:
They are the linear equations.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
If the lines have the same slope, they are parallel and the system of equations has no solution.
If the lines have the same equations, the system of equations has infinitely many solutions.
If the lines have different slopes, the system of equations has one solution.
We have slopes:
We have the slopes:
[tex]y=x+1\to m_1=1\\\\y=2x-5\to m_2=2[/tex]
Different the slopes. Therefore the system has one solution.
Solution:
[tex]\text{Substitute}\ y=x+1\ \text{to the second equation}\ y=2x-5:\\\\x+1=2x-5\qquad\text{subtract 1 from both sides}\\\\x=2x-6\qquad\text{subtract 2x from both sides}\\\\-x=-6\qquad\text{change the signs}\\\\\boxed{x=6}\\\\\text{Put the value of x to the first equation:}\\\\y=6+1\\\\\boxed{y=7}\\\\\boxed{\boxed{x=6,\ y=7\to(6,\ 7)}}[/tex]
