Solution
Step 1:
There are three types of systems of linear equations in two variables, and three types of solutions.
1. An independent system has exactly one solution pair. The point where the two lines intersect is the only solution.
2. An inconsistent system has no solution.
3. A dependent system has infinitely many solutions.
Step 2
Solve the systems of the equations using the substitution method
Final answer
The system is dependent so there are infinite solutions.
Equivalent
We have the isosceles triangle were y + 12 = 3x - 5,
and the equilateral triangle. Therefore 3x - 5 = 5y - 4.
From the first equation and the second equation we have:
y + 12 = 5y - 4 <em>subtract 12 from both sides</em>
y = 5y - 16 <em>subtract 5y from both sides</em>
-4y = -16 <em>divide both sides by (-4)</em>
<h3>y = 4</h3>
Substitute the value of y to the first equation:
4 + 12 = 3x - 5
16 = 3x - 5 <em>add 5 to both sides</em>
21 = 3x <em>divide both sides by 3</em>
<h3>x = 7</h3>
<h3>Answer: x = 7 and y = 4</h3>
Since angle CDA + angle ABC = 180 then DC is Parallel to AB by transversal of parallel line theorem c-pattern for co-interior angles. to help visualize it draw it
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