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3 years ago

1) 2x + y = 12 x + 2y = 9 Solve the following systems algebraically and check

Mathematics

1 answer:

Kaylis [27]3 years ago

6 0

Answer: x = 5, y = 2; Solution = (5, 2)

Step-by-step explanation:

Substitution

2x + y = 12

x + 2y = 9

Subtract 2y from both sides

x = 9 - 2y

Now, substitute x for (9 - 2y) in the first equation

2x + y = 12

2 (9 - 2y) + y = 12

Distribute 2

18 - 4y + y = 12

18 - 3y = 12

Subtract 18 from both sides

-3y = -6

Divide both sides by -3

y = 2

Now to find x, substitute 2 for y in (x = 9 - 2y)

x = 9 - 2y

x = 9 - 2(2)

x = 9 - 4

x = 5

Solution: (5, 2)

Elimination

2x + y = 12

x + 2y = 9

Multiply the second equation by -2 to find y

2x + y = 12

(x + 2y = 9) -2

2x + y = 12

-2x - 4y = -18

Add both equations

2x and -2x are cancelled out

You get:

-3y = -6

Divide both sides by -3

y = 2

Substitute 2 for y in any of the equations to find x

I chose x + 2y = 9

x + 2y = 9

x + 2 (2) = 9

x + 4 = 9

Subtract both sides by 4

x = 5

Solution = (5, 2)

Btw you can use any of these methods, I used both so you could know that you get the same answer no matter the method.

Hope I helped!

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Consider the system of inequalities

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$\left\{ \begin{array}{l} y=2 \text{ (red line)} \\ x= 6 \text{ (blue line)}\\ y=3x+2 \text{ (green line)} \\ y= -x+10 \text{ (orange line)}. \end{array}\right.$

2. Determine which bounded part of the plane you should select:

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for $y\le -x+10$ you can check where the origin is placed. Since $0\le -1\cdot 0+10$ , the origin belongs to the needed part and you have to take the bottom part of the coordinate plane that was formed by orange line.

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3 years ago

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babunello [35]

Answer:

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Step-by-step explanation:

Let the first number be x, and the second number be y.

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x - y = 4

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