Question

Решите систему способом подстановки: 1)3x+4y=1 5x-y=6 2)x+2y=-1 3x-4y=17 3)3x-y=-1 -2x+3y=-11 4)2x=y=4 x-1/3y=-3

Answer 1

Объяснение:

4-й пример не сильно понял, так что написал как смог решить.

Answer 2

1. Let's solve the first system of equations using the method of substitution:

Given equations:

1. 3x + 4y = 1
2. 5x - y = 6

We can rearrange equation 2 to express y in terms of x: y = 5x - 6

Now substitute this value of y into equation 1: 3x + 4(5x - 6) = 1

Simplifying the equation: 3x + 20x - 24 = 1 23x - 24 = 1 23x = 25 x = 25/23

Substitute the value of x back into equation 2 to find y: 5(25/23) - y = 6 125/23 - y = 6 y = 125/23 - 6 y = 125/23 - 138/23 y = -13/23

Therefore, the solution to the first system of equations is x = 25/23 and y = -13/23.

2. Let's solve the second system of equations using the method of substitution:

Given equations:

1. x + 2y = -1
2. 3x - 4y = 17

We can rearrange equation 1 to express x in terms of y: x = -1 - 2y

Now substitute this value of x into equation 2: 3(-1 - 2y) - 4y = 17

Simplifying the equation: -3 - 6y - 4y = 17 -10y - 3 = 17 -10y = 20 y = 20/-10 y = -2

Substitute the value of y back into equation 1 to find x: x + 2(-2) = -1 x - 4 = -1 x = -1 + 4 x = 3

Therefore, the solution to the second system of equations is x = 3 and y = -2.

3. Let's solve the third system of equations using the method of substitution:

Given equations:

1. 3x - y = -1
2. -2x + 3y = -11

We can rearrange equation 1 to express y in terms of x: y = 3x + 1

Now substitute this value of y into equation 2: -2x + 3(3x + 1) = -11

Simplifying the equation: -2x + 9x + 3 = -11 7x + 3 = -11 7x = -14 x = -14/7 x = -2

Substitute the value of x back into equation 1 to find y: 3(-2) - y = -1 -6 - y = -1 y = -1 + 6 y = 5

Therefore, the solution to the third system of equations is x = -2 and y = 5.

4. It seems there is an error in the fourth system of equations. The equation 4) 2x = y = 4 contains two equal signs, which is not valid. Please provide the correct equation, and I will be happy to help you solve it.