5х-у=7 3х+2у=-1

To solve the system of equations:

5x - y = 7 .......(1) 3x + 2y = -1 .......(2)

We can solve this system of equations by using the method of substitution or elimination.

Method of substitution: Step 1: Solve one equation for one variable in terms of the other variable. From equation (1), we can rearrange it to solve for y: y = 5x - 7

Step 2: Substitute this value of y into the second equation (2). 3x + 2(5x - 7) = -1 3x + 10x - 14 = -1 13x - 14 = -1

Step 3: Solve for x: 13x = -1 + 14 13x = 13 x = 1

Step 4: Substitute the value of x back into one of the original equations to solve for y: 5(1) - y = 7 5 - y = 7 -y = 7 - 5 -y = 2 y = -2

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

Method of elimination: Step 1: Multiply equation (1) by 2 and equation (2) by -1 to eliminate y: 10x - 2y = 14 -3x - 2y = 1

Step 2: Add the two equations together to eliminate y: (10x -2y) + (-3x -2y) = 14 + 1 10x -2y -3x -2y = 15x = 15 7x = 15 x = 15/7

Step 3: Substitute the value of x back into one of the original equations to solve for y: 5(15/7) - y = 7 75/7 - y = 7 75 - 7y = 49 -7y = 49 - 75 -7y = -26 y = -26/-7 y = 26/7

So the solution to the system of equations is x = 15/7 and y = 26/7.