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Determine if the equations are intersecting, parallel, or coincident.

bx - ay = 2
ax + by = 3

User Jpihl
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2 Answers

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Answer

Parallel

Explanation:

User KajMagnus
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2 votes
Since bx does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting bx from both sides.
-ay=-bx+2
ax+by=3

Divide each term in the equation by -1a.
y=(bx-2)/(a)
ax+by=3

Divide each term in the numerator by the denominator.
y=(bx)/(a)-(2)/(a)
ax+by=3

The equation is not linear, so the slope does not exist.
No slope can be found.
ax+by=3

Since ax does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting ax from both sides.
No slope can be found.
by=-ax+3

Remove the common factors that were cancelled out.
No slope can be found.
y=-(ax)/(b)+(3)/(b)

Divide each term in the equation by b.
No slope can be found.
y=(-ax+3)/(b)

Divide each term in the numerator by the denominator.
No slope can be found.
y=-(ax)/(b)+(3)/(b)

The equation is not linear, so the slope does not exist.
No slope can be found.
No slope can be found.

Compare the slopes (m) of the two equations.
m1=, m2=

The equations are parallel because the slopes of the two lines are equal.
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User Floum
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