<span>4x + 3y = 16
7x + 6y = 31
Note what happens if we mult. the first eqn. by -2:
-8x - 6y = -32
Combining this with the 2nd equation eliminates the variable y:
</span>-8x - 6y = -32<span>
7x + 6y = 31
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-x = -1, or x = 1. Sub 1 for x in either of the 2 given eqns to find y:
For example: 4(1) + 3y = 16, so 36 = 12, and y = 3. Sol'n is (1,3).</span>
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1. Quadrilateral ABCD is inscribed in circle O
A quadrilateral is a four sided figure, in this case ABCD is a cyclic quadrilateral such that all its vertices touches the circumference of the circle.
A cyclic quadrilateral is a four sided figure with all its vertices touching the circumference of a circle.
2. mBCD = 2 (m∠A) = Inscribed Angle Theorem
An inscribed angle is an angle with its vertex on the circle, formed by two intersecting chords.
Such that Inscribed angle = 1/2 Intercepted Arc
In this case the inscribed angle is m∠A and the intercepted arc is MBCD
Therefore; m∠A = 1/2 mBCD
4. The sum of arcs that make up a circle is 360
Therefore; mBCD + mDAB = 360°
The circles is made up of arc BCD and arc DAB, therefore the sum angle of the arcs is equivalent to 360°
5. 2(m∠A + 2(m∠C) = 360; this is substitution property
From step 4 we stated that mBCD +mDAB = 360
but from the inscribed angle theorem;
mBCD= 2 (m∠A) and mDAB = 2(m∠C)
Therefore; substituting in the equation in step 4 we get;
2(m∠A) + 2(m∠C) = 360
I don't understand the question. Can I have some context?
