Determine whether the statement is always, sometimes, or never true. If △ABC has angles that measure 10° and 40°, and △DEF has a
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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.
<u>Slope-intercept form</u>
y = mx + b
m ... slope
b ... y-intercept
If two lines have the <em>same slope </em>but <em>different y-intercept</em>, they are parallel - <u>system has no solutions</u>.
If two lines have the <em>same slope</em> and the <em>same y-intercept</em>, they are the same line and are intersecting in infinite many points - <u>system has infinite many solutions</u>.
If two lines have <em>different slopes</em> then they intersect in one point - <u>system has one solution</u>.
We see that lines have different slopes. First line has slope 1 and the other line has slope . 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