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alexandr402 [8]
2 years ago
15

13. Find the solution to the following system of equations using any method: 4x - y = 3 -4x + y = -3

Mathematics
1 answer:
forsale [732]2 years ago
3 0

Start by writing out the system of equations.

  • 4x - y = 3
  • -4x + y = -3

The easiest way to solve this system of equations is the elimination method. This is because both equations contain opposites of each other that you can cancel out.

Add the system of equations together. After adding, everything cancels out. 4x + (-4x) = 0 ; -y + y = 0 ; 3 + (-3) = 0.

You are left with the equation of 0 = 0. Since this is a TRUE statement, this means that there are infinitely many solutions to this system of equations.

If you were left with a false statement, for example 4 = 0, then the answer would be "no solution".

Another way to solve this system of equations is by the substitution method. This method works best if you are given a system of equations with one variable clearly defined.

For example, the system of equations could be:

  • 4x - y = 3
  • y = 3x + 4

y is equal to 3x + 4, so you could easily substitute y into the first equation. The elimination method wouldn't be the best choice because the system of equations are in the standard form Ax + By = C.

Generally any system of equations in the standard form are easier to solve using the elimination method. Hope this helped, good luck!

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3x2 - 5x + 6) + (9 - 8x - 4x2)
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13-13x

Step-by-step explanation:

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MN is a diameter of a circle with centre ' O ' . If BD = CD , prove that ∠OAD = ∠OCD
Varvara68 [4.7K]

Answer:

\sf \: Proved \: \angle \: OAD  \:  =  \angle \: OCD

Step-by-step explanation:

<em>Given:</em>

Mn is diameter of circle having centre O

and BD = OD,

<em><u>To prove that:</u></em>

<u>\angle \: OAD  \:  =  \angle \: OCD</u>

<em>Solution:</em>

Join the points O and B and draw OB,

On joining the line,

in ∆OCD and ∆OBD,

OC =OB → (Radius of same circle)

BD =CD → (from given)

OD =OD → (Common side in both the triangles)

Hence ∆OCD and ∆OBD are congruent from SSS property.

so we can say that,

\angle \: OBD  \:  =  \angle \: OCD

Consider above prove as statement A

Corresponding angles of congruent traingle.

in ∆ OAB,

OA = OB (radius of same circle)

hence ∆OAB is an isosceles traingle.

We know that opposite angle of isosceles traingle are always equal. hence,

\angle \: OBD  \:  =  \angle \: OAB \\ \angle \: OAB  \:  =  \angle \: OAD (same \: angles) \\ \angle \: OBD  \:  =  \angle \: OAD

Consider above prove as statement B

From Statement A & B we can say that

\angle \: OAD  \:  =  \angle \: OCD

<em>Thanks for joining brainly community!</em>

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2 years ago
3x + 3 = 2x + 12 i need help for this answer
Flura [38]

Answer:

x=9

Step-by-step explanation:

6 0
2 years ago
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