Question

(1216. Решите способом подстановки систему уравнений: 1) | 4x+3y=5, y-2x=-5; 2) {7y-2x=20; 3) (8x-5y=0, | 5x-3y=1; 4) 7x-y=13, 5y+16x=-14; 5) J 6y+5x=9, 2x+3y-6; 6) (2x-9y-36, 6y+7x=51.​ Смотреть ответ olesya261184 olesya261184 Пошаговое объяснение:ответ дан проверин экспертом

Answer 1

System of Equations: 1) 4x + 3y = 5, y - 2x = -5

To solve this system of equations using the method of substitution, we'll start by solving one equation for one variable and then substituting that expression into the other equation.

Let's solve the second equation, y - 2x = -5, for y: y = 2x - 5

Now, substitute this expression for y in the first equation: 4x + 3(2x - 5) = 5

Simplify and solve for x: 4x + 6x - 15 = 5 10x - 15 = 5 10x = 20 x = 2

Now, substitute the value of x back into the second equation to find y: y - 2(2) = -5 y - 4 = -5 y = -1

Therefore, the solution to the system of equations 4x + 3y = 5 and y - 2x = -5 is x = 2 and y = -1.

System of Equations: 2) 7y - 2x = 20, 8x - 5y = 0

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

Let's solve the first equation, 7y - 2x = 20, for y: 7y = 2x + 20 y = (2x + 20)/7

Now, substitute this expression for y in the second equation: 8x - 5((2x + 20)/7) = 0

Simplify and solve for x: 8x - (10x + 100)/7 = 0 (56x - 10x - 100)/7 = 0 (46x - 100)/7 = 0 46x - 100 = 0 46x = 100 x = 100/46 x ≈ 2.17

Now, substitute the value of x back into the first equation to find y: 7y - 2(2.17) = 20 7y - 4.34 = 20 7y = 24.34 y ≈ 3.48

Therefore, the solution to the system of equations 7y - 2x = 20 and 8x - 5y = 0 is x ≈ 2.17 and y ≈ 3.48.

System of Equations: 3) 7x - y = 13, 5y + 16x = -14

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

Let's solve the first equation, 7x - y = 13, for y: y = 7x - 13

Now, substitute this expression for y in the second equation: 5(7x - 13) + 16x = -14

Simplify and solve for x: 35x - 65 + 16x = -14 51x - 65 = -14 51x = 51 x = 1

Now, substitute the value of x back into the first equation to find y: 7(1) - y = 13 7 - y = 13 -y = 6 y = -6

Therefore, the solution to the system of equations 7x - y = 13 and 5y + 16x = -14 is x = 1 and y = -6.

System of Equations: 4) 5x - 3y = 1, 7x - y = 13

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

Let's solve the second equation, 7x - y = 13, for y: y = 7x - 13

Now, substitute this expression for y in the first equation: 5x - 3(7x - 13) = 1

Simplify and solve for x: 5x - 21x + 39 = 1 -16x + 39 = 1 -16x = -38 x = -38/-16 x ≈ 2.375

Now, substitute the value of x back into the second equation to find y: 7(2.375) - y = 13 16.625 - y = 13 -y = 13 - 16.625 -y = -3.625 y ≈ 3.625

Therefore, the solution to the system of equations 5x - 3y = 1 and 7x - y = 13 is x ≈ 2.375 and y ≈ 3.625.

System of Equations: 5) 6y + 5x = 9, 2x + 3y = 6

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

Let's solve the second equation, 2x + 3y = 6, for x: 2x = 6 - 3y x = (6 - 3y)/2

Now, substitute this expression for x in the first equation: 6y + 5((6 - 3y)/2) = 9

Simplify and solve for y: 6y + (30 - 15y)/2 = 9 12y + 30 - 15y = 18 -3y = -12 y = 4

Now, substitute the value of y back into the second equation to find x: 2x + 3(4) = 6 2x + 12 = 6 2x = -6 x = -3

Therefore, the solution to the system of equations 6y + 5x = 9 and 2x + 3y = 6 is x = -3 and y = 4.

System of Equations: 6) 2x - 9y = 36, 6y + 7x = 51

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

Let's solve the first equation, 2x - 9y = 36, for x: 2x = 36 + 9y x = (36 + 9y)/2

Now, substitute this expression for x in the second equation: 6y + 7((36 + 9y)/2) = 51

Simplify and solve for y: 6y + (252 + 63y)/2 = 51 12y + 252 + 63y = 102 75y = -150 y = -2

Now, substitute the value of y back into the first equation to find x: 2x - 9(-2) = 36 2x + 18 = 36 2x = 18 x = 9

Therefore, the solution to the system of equations 2x - 9y = 36 and 6y + 7x = 51 is x = 9 and y = -2.

I hope this helps! Let me know if you have any further questions.