Question

2x-y=5 3x+2y=4 Система уравнений

Answer 1

2x-y=5
3x+2y=4

у=2х-5
3х+2(2х-5)=4
3х+4х-10=4
7х=14
х=2

2*2-у=5
4-у=5
у=-1

Answer 2

$\left \{ {{2x-y=5} /*2\atop {3x+2y=4}} \right. \left \{ {{4x-2y=10} \atop {3x+2y=4}} \right. \\ 7x=14\\x=2\\8-2y=10\\-2y=10-8\\-2y=2\\y=-1 \\ \\ \left \{ {{x=2} \atop {y=-1}} \right.$

Answer 3

Solving the System of Equations

To solve the system of equations 2x - y = 5 and 3x + 2y = 4, we can use various methods such as substitution, elimination, or matrix methods. Let's solve it using the elimination method.

To eliminate the variable y, we can multiply the first equation by 2 and the second equation by 1, and then add the two equations together. This will eliminate the y variable.

Multiplying the first equation by 2 gives us: 4x - 2y = 10.

Multiplying the second equation by 1 gives us: 3x + 2y = 4.

Adding the two equations together eliminates the y variable: 7x = 14.

Dividing both sides of the equation by 7 gives us: x = 2.

Now, we can substitute the value of x back into one of the original equations to solve for y.

Substituting x = 2 into the first equation 2x - y = 5 gives us: 2(2) - y = 5.

Simplifying the equation gives us: 4 - y = 5.

Subtracting 4 from both sides of the equation gives us: -y = 1.

Multiplying both sides of the equation by -1 gives us: y = -1.

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

Solution:

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