X-y=-10 2x+3y=15

To solve this system of equations, we can use the method of substitution or elimination.

Method 1: Substitution

1. Solve the first equation for x in terms of y: x = -10 + y

2. Substitute x in the second equation with (-10 + y): 2(-10 + y) + 3y = 15

3. Simplify the equation: -20 + 2y + 3y = 15 5y - 20 = 15

4. Move the constant term to the other side: 5y = 15 + 20 5y = 35

5. Divide both sides of the equation by 5: y = 7

6. Substitute the value of y into the first equation to find x: x - 7 = -10 x = -10 + 7 x = -3

So, the solution to the system of equations is x = -3 and y = 7.

Method 2: Elimination

1. Multiply the first equation by 2 and the second equation by -1 to make the coefficients of x in both equations the same: 2(x - y) = 2(-10) -2x - 3y = -15

2. Add the modified equations together to eliminate x: (2x + 3y) + (-2x - 3y) = 15 + (-15) 0 = 0

The resulting equation 0 = 0 indicates that the two equations are dependent and represent the same line. Thus, there are infinitely many solutions to the system of equations.

In either case, the solution is x = -3 and y = 7.