Question

2x+y=114 * ( 2x + 5 ) = 60 - (2y + 2)

Answer 1

Ответ:

{(4; 3)}

Пошаговое объяснение:

$\left \{ {{2x+y=11} \atop {4*(2x+5)=60-(2y+2)}} \right. \\\left \{ {{y=11-2x} \atop {8x+20=60-(2(11-2x)+2)}} \right. \\\left \{ {{y=11-2x} \atop {8x+20=60-22+4x-2}} \right. \\\left \{ {{y=11-2x} \atop {8x-4x=36-20}} \right. \\\left \{ {{y=11-2x} \atop {4x=16}} \right. \\\left \{ {{y=11-2*4} \atop {x=4}} \right. \\\left \{ {{y=3} \atop {x=4}} \right.$

Проверка:

2·4+3=11 верно

4·(2·4+5)=60-(2·3+2)

4·13=52

52=52 верно

Answer 2

To solve the system of equations:

2x + y = 114 ...(Equation 1) 2x + 5 = 60 - (2y + 2) ...(Equation 2)

Let's solve it step by step:

First, let's simplify Equation 2:

2x + 5 = 60 - 2y - 2

Now, combine like terms:

2x + 5 = 58 - 2y

Rearrange the equation:

2x + 2y = 58 - 5

2x + 2y = 53 ...(Equation 3)

We now have a system of two equations:

2x + y = 114 ...(Equation 1) 2x + 2y = 53 ...(Equation 3)

To eliminate the variable x, we'll multiply Equation 1 by -2:

-2(2x + y) = -2(114) -4x - 2y = -228 ...(Equation 4)

Now, we can subtract Equation 4 from Equation 3:

(2x + 2y) - (-4x - 2y) = 53 - (-228)

Simplifying further:

2x + 2y + 4x + 2y = 53 + 228 6x + 4y = 281 ...(Equation 5)

Now we have a new equation:

6x + 4y = 281 ...(Equation 5)

To solve for x, we can multiply Equation 5 by -1.5:

-1.5(6x + 4y) = -1.5(281) -9x - 6y = -421.5 ...(Equation 6)

Next, we'll subtract Equation 6 from Equation 5:

(6x + 4y) - (-9x - 6y) = 281 - (-421.5)

Simplifying further:

6x + 4y + 9x + 6y = 281 + 421.5 15x + 10y = 702.5

Divide both sides of the equation by 5 to simplify it further:

3x + 2y = 140.5 ...(Equation 7)

Now we have another equation:

3x + 2y = 140.5 ...(Equation 7)

We have simplified the system of equations to:

2x + y = 114 ...(Equation 1) 3x + 2y = 140.5 ...(Equation 7)

To solve this system of equations, we can use various methods such as substitution or elimination. Let's solve it using the elimination method:

Multiply Equation 1 by 2:

2(2x + y) = 2(114) 4x + 2y = 228 ...(Equation 8)

Now, subtract Equation 8 from Equation 7:

(3x + 2y) - (4x + 2y) = 140.5 - 228

Simplifying further:

3x + 2y - 4x - 2y = -87.5

Combine like terms:

3x - 4x = -87.5

-x = -87.5

Divide both sides of the equation by -1:

x = 87.5

Substitute the value of x into Equation 1:

2(87.5) + y = 114

175 + y = 114

Subtract 175 from both sides of the equation:

y = 114 - 175

y = -61

Therefore, the solution to the system of equations is x = 87.5 and y = -61.