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VashaNatasha [74]
3 years ago
9

Simultaneous Equations: Find the two intersects of x^2 + y^2 = 25 and y = 2x - 2

Mathematics
1 answer:
Yakvenalex [24]3 years ago
7 0
X^2 + y^2 = 25 (1)
y = 2x - 2 (2)

Subs (2) into (1)

x^2 + (2x - 2)^2 = 25
• Expand the eq like below

x^2 + (2x-2)(2x-2) = 25

x^2 + 4x^2 + 4x - 4x + 4 = 25
• Cancel out 4x-4x which is equals to zero

5x^2 = 25
• Divide both sides with 5

x^2 = 5
• To remove the square (^2) on the x, you need to square root both sides

x = 5 or x = -5

Subs x = 5 and x = -5 into (2)

y = 2x - 2
y = 2(5) - 2 = 10 - 2 = 8

y = 2x - 2
y = 2(-5) - 2 = -10 - 2 = -12

Therefore the intersection points are:

x=5, y= 8
x= -5, y= -12
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Now we will find the value of y.

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Hope this helps :)
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<h3><u>Answer:</u></h3>

\large\boxed{\pink{\sf \leadsto Value \ of \ LM \ is \ 11 \ units . }}

<h3><u>Step-by-step explanation:</u></h3>

A figure is given to us in which we can see two triangles one is ∆ MPL and other is ∆MPN .

<u>Figure</u><u> </u><u>:</u><u>-</u><u> </u>

\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\linethickness{0.25mm}\put(0,0){\line(1,2){2}} \put(0.001,0){\line(1,0){4}}\put(2,0){\vector(0,1){5}}\put(4,0){\line( - 1,2){2}}\put(0,-0.4){$\bf L $}\put(2,-0.4){$\bf P$}\put(4,-0.4){$\bf N $}\put(2.2,4){$\bf M $}\put(2.8, - .4){$\bf 5 $}\put(1, - .4){$\bf 5 $}\put(3.4, 2){$\bf 11 $}\put(2.3,0){\line(0,1){.3}}\put(2.3,.3){\line( - 1,0){.3}}\end{picture}

\underline{\blue{\sf In\: \triangle MPL \ \& \ \triangle MPN :- }}

\qquad \bullet LP = PN = 5 \:\:(given) \\\\\qquad \bullet MP = MP \:\:(Common) \\\\\qquad \bullet \angle MPN = \angle MPL = 90^{\circ} \:\: (given)

Hence by SAS congruence condition ,

\orange{\bf \triangle MPL \cong \triangle MPN }

Hence by cpct ( Corresponding parts of congruent triangles ) we can say that , LM = NM = 11 units .

<h3><u>Hence </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>LM</u><u> </u><u>is</u><u> </u><u>1</u><u>1</u><u> </u><u>units</u><u> </u><u>.</u></h3>
4 0
2 years ago
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