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3 years ago

30 POINTS! What is the first step to solve the following system of equations using substitution?

Mathematics

2 answers:

Artyom0805 [142]3 years ago

4 0

Answer:

add the 2 equations together

allochka39001 [22]3 years ago

3 0

Answer:

The answer to your question would be C.

Step-by-step explanation:

Substitution method can be applied in four steps

Step 1:

Solve one of the equations for either x = or y = .

Step 2:

Substitute the solution from step 1 into the other equation.

Step 3:

Solve this new equation.

Step 4:

Solve for the second variable.

Example 1: Solve the following system by substitution

2x+3yx+y=5=5

Solution:

Step 1: Solve one of the equations for either x = or y = . We will solve second equation for y.

x+yy=5=5−x

Step 2: Substitute the solution from step 1 into the second equation.

2x+3y2x+3(5−x)=5=5

Step 3: Solve this new equation.

2x+3(5−x)2x+15−3x−x+15−xx=5=5=5=5−15=10

Step 4: Solve for the second variable

yyy=5−x=5−10=−5

The solution is: (x, y) = (10, -5)

Note: It does not matter which equation we choose first and which second. Just choose the most convenient one first!

Example 2: Solve by substitution

2x+5y4x−y=12=2

Solution:

Step 1: Solve one of the equations for either x = or y =. Since the coefficient of y in equation 2 is -1, it is easiest to solve for y in equation 2.

4x−y−yy=2=2−4x=4x−2

Step 2: Substitute the solution from step 1 into the second equation.

2x+5y2x+5(4x−2)=12=12

Step 3: Solve this new equation ( for x ).

2x+5(4x−2)2x+2x+20x−1022xx=12=12=22=1

Step 4: Solve for the second variable

yyy=4x−2=4⋅x−2=2

The solution is: (x,y)=(1,2)

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3 years ago

A hole is punched in a piece of metal to make a part for a machine.

Llana [10]

Given:

The length of the side of the metal is x + 7.

The length of the side of the hole is x - 2.

We need to determine the area of the metal part or the shaded region.

Area of the metal:

The area of the metal can be determined using the formula,

$A=s^2$

Substituting s = x + 7, we get;

$A=(x+7)^2$

$A=x^2+14x+49$

Thus, the area of the metal is $x^2+14x+49$ square units.

Area of the hole:

The area of the hole can be determined using the formula,

$A=s^2$

Substituting s = x -2 ,we get;

$A=(x-2)^2$

$A=x^2-4x+4$

Thus, the area of the hole is $x^2-4x+4$ square units.

Area of the shaded region:

The area of the shaded region can be determined by subtracting the area of the hole from the area of the metal.

Thus, we have;

Area = Area of the metal - Area of the hole

Substituting the values, we have;

$Area = x^2+14x+49-(x^2-4x+4)$

Simplifying, we have;

$Area = x^2+14x+49-x^2+4x-4$

$Area = 18x+45$

Thus, the area of the shaded region is (18x + 45) square units.

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3 years ago

Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number

Dmitry [639]

Answer:

Part a) $2,50,18$

Part b) When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For $x=2$

$\sqrt{2}*\sqrt{2}=\sqrt{4}=2$ -----> the product is an integer

The number $x=2$ could be Jenny favorite positive integer

2) For $x=50$

$\sqrt{50}*\sqrt{2}=\sqrt{100}=10$ -----> the product is an integer

The number $x=50$ could be Jenny favorite positive integer

3) For $x=18$

$\sqrt{18}*\sqrt{2}=\sqrt{36}=6$ -----> the product is an integer

The number $x=18$ could be Jenny favorite positive integer

Part B)

1) For $x=2$

$\sqrt{2}/\sqrt{2}=\sqrt{1}=1$ -----> the result is an integer

2) For $x=50$

$\sqrt{50}/\sqrt{2}=\sqrt{25}=5$ -----> the result is an integer

3) For $x=18$

$\sqrt{18}/\sqrt{2}=\sqrt{9}=3$ -----> the result is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

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3 years ago