Question

X-2y=3 3x+2y=1 2x-y=4 3x+7y=1

Answer 1

1)3x+2y=1
x=3+2y

x=3+2y
3(3+2y)+2y=1

x=3+2y
9+6y+2y=1

x=3+2y
8y=1-9

x=3+2y
y=-8/8

x=3+2y
y=-1

y=-1
x=3+2×(-1)

y=-1
x=3-2

y=-1
x=1

2)3x+7y=1
-y=4-2x

3x+7y=1
y=-4+2x

y=-4+2x
3x+7(-4+2x)=1

y=-4+2x
3x-28+14x=1

y=-4+2x
-11x=29

и тд

Answer 2

To solve this system of equations:

Equation 1: X - 2y = 3 Equation 2: 3x + 2y = 1 Equation 3: 2x - y = 4 Equation 4: 3x + 7y = 1

We can use various methods, such as substitution or elimination. Let's solve this system using the elimination method.

First, let's add Equation 2 and Equation 4 to eliminate the "x" term: (3x + 2y) + (3x + 7y) = 1 + 1 6x + 9y = 2

Now, let's multiply Equation 1 by 3 and Equation 3 by 2 to obtain equivalent coefficients for "x": 3(X - 2y) = 3(3) 2(2x - y) = 2(4)

Expanding those equations, we get: 3x - 6y = 9 4x - 2y = 8

Next, we'll add the last two equations to eliminate the "y" term: (4x - 2y) + (3x - 6y) = 8 + 9 7x - 8y = 17

So far, we have the following system: 6x + 9y = 2 7x - 8y = 17

To eliminate "y," we can multiply the first equation by 8 and the second equation by 9: 8(6x + 9y) = 8(2) 9(7x - 8y) = 9(17)

Expanding those equations, we get: 48x + 72y = 16 63x - 72y = 153

Adding these two equations eliminates the "y" term: (48x + 72y) + (63x - 72y) = 16 + 153 111x = 169

Now, let's solve for "x": x = 169/111

Substituting this value back into one of the previous equations, such as Equation 1, we can solve for "y": X - 2y = 3 169/111 - 2y = 3 -2y = 3 - 169/111 -2y = (333 - 169)/111 -2y = 164/111

Simplifying further: y = (164/111) / (-2) y = (164/111) * (-1/2) y = -82/111

Therefore, the solution to the system of equations is: x ≈ 1.523 (rounded to three decimal places) y ≈ -0.739 (rounded to three decimal places)