Question

Решить систему 1) 3x+2y=7 2) x-2y=-3

Answer 1

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

из второго уравнения системы следует, что
2у=х+3

подставляем это выражение в первое уравнение :

3х+х+3=7
4х=4
х=1

подставляем это значение в первое уравнение
3+2у=7
2у=4
у =2

Ответ х=1 ,у=2

Answer 2

3x+2y=7 2y и -2y уходят.
x-2y=-3 остается:


3x+x=7+(-3)
4x=4

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

Answer 3

To solve the system of equations:

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

We can use either the substitution method or the elimination method. Let's use the elimination method:

Step 1: Multiply both sides of equation 2 by 2 to make the coefficients of y in both equations the same: 2(x - 2y) = 2(-3) 2x - 4y = -6

Now, the system becomes:

1. 3x + 2y = 7
2. 2x - 4y = -6

Step 2: Now, we can eliminate y by adding the two equations together: (3x + 2y) + (2x - 4y) = 7 + (-6) 5x - 2y = 1

Step 3: Now, let's eliminate y again by adding the original equation 1 to the new equation we obtained: (3x + 2y) + (5x - 2y) = 7 + 1 8x = 8

Step 4: Solve for x: x = 8 / 8 x = 1

Step 5: Now that we have the value of x, we can find y by substituting the value of x into either equation 1 or 2. Let's use equation 1: 3(1) + 2y = 7 3 + 2y = 7

Step 6: Solve for y: 2y = 7 - 3 2y = 4 y = 4 / 2 y = 2

So, the solution to the system of equations is x = 1 and y = 2.