Question

3/5x+1/25y=32 7/50-9/10y=-38

Answer 1

Ответ:

(50; 50)

Пошаговое объяснение:

{3/5х + 1/25у = 32 | * 25

{7/50х - 9/10у = -38 | * 50

{15х + у = 800

{7х - 45у = -1900

{у = 800 - 15х

{7х - 45у = -1900

1)

7х - 45у = -1900

7х - 45(800 - 15х) = -1900

7х - 36000 + 675х = -1900

682х = -1900 + 36000

682х = 34100

х = 34100 : 682

х = 50

2)

у = 800 - 15х

у = 800 - 15 * 50

у = 800 - 750

у = 50

(50; 50)

Answer 2

To solve the system of equations:

Equation 1: (3/5)x + (1/25)y = 32 Equation 2: (7/50) - (9/10)y = -38

Let's solve it step by step:

Step 1: Simplify Equation 2 Multiply all terms in Equation 2 by 50 to eliminate the denominators: 50 * [(7/50) - (9/10)y] = 50 * (-38) 7 - 9y = -1900

Step 2: Solve for y Add 9y to both sides of the equation to isolate the term: 7 - 9y + 9y = -1900 + 9y 7 = -1900 + 9y

Simplify the right side: 7 = 9y - 1900

Add 1900 to both sides: 7 + 1900 = 9y - 1900 + 1900 1907 = 9y

Divide both sides by 9: 1907/9 = 9y/9 y = 1907/9

Step 3: Substitute the value of y into Equation 1 Substitute y = 1907/9 into Equation 1: (3/5)x + (1/25)*(1907/9) = 32

Simplify the expression: (3/5)x + 1907/225 = 32

Multiply through by the least common denominator (225) to eliminate fractions: 225*(3/5)x + 225*(1907/225) = 225*32 135x + 1907 = 7200

Step 4: Solve for x Subtract 1907 from both sides of the equation to isolate the term: 135x + 1907 - 1907 = 7200 - 1907 135x = 5293

Divide both sides by 135: 135x/135 = 5293/135 x = 5293/135

Step 5: Final Result The solution to the system of equations is: x = 5293/135 y = 1907/9