Answer:
This linear system has one solution.
Step-by-step explanation:
First equation: y = x + 2
Second equation: 6x - 4y = -10
Let's change the second equation in slope-intercept form y = mx + b.
Slope-intercept form
y = mx + b
m ... slope
b ... y-intercept
[tex]6x - 4y = -10[/tex]
[tex]6x + 10 = 4y[/tex]
[tex]\frac{6}{4}x + \frac{10}{4} = y[/tex]
[tex]\frac{3}{2}x + \frac{5}{2} = y[/tex]
If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.
If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.
If two lines have different slopes then they intersect in one point - system has one solution.
We see that lines have different slopes. First line has slope 1 and the other line has slope [tex]\frac{3}{2}[/tex]. So the system has one solution.
You can also check this by solving the system.
Substitute y in second equation with y from first.
6x - 4y = -10
6x - 4(x + 2) = -10
Solve for x.
6x - 4x - 8 = -10
2x = -2
x = -1
y = x + 2
y = -1 + 2
y = 1
The lines intersect in point (-1, 1). <-- one solution
