**Question 1: **Solve the system of equations:

2x + 3y = -5

4x - y = 10

** Solution: **

Given equations are

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

4x - y = 10 ......(2)

Isolate the variable x using below steps

2x + 3y = -5

2x = -5 - 3y

x = $\frac{-(5 + 3y)}{2}$

Substitute the value of x from (1) in (2) to get

4 $\frac{-(5 + 3y)}{2}$ - y = 10

2(-5 - 3y) - y = 10

-10 -6y - y = 10

-7y = 10 + 10

y = - $\frac{20}{7}$

y = -2.857

Substitute the value of y in (1) to get

2x + 3y = -5

2x + 3(-2.857) = -5

2x = -5 + 8.571

x = $\frac{3.571}{2}$

x = 1.7855

The solution for the given system of equations are (x,y) = (1.786, -2.857).

**Question 2: **Solve the set of equations:

5x + y = -5

5x - 4y = 4.

** Solution: **

Given equations are

5x + y = -5 .....(1)

5x - 4y = 4 ......(2)

Isolate the value of x in (1) to get

5x + y = -5

5x = -5 - y

x = $\frac{-(5 + y)}{5}$

Substitute the value of x from (1) in (2) to get

5x - 4y = 4

5 $\frac{-(5 + y)}{5}$ - 4y = 4

-5 - y - 4y = 4

-5 - 5y = 4

-5y = 4 + 5

-5y = 9

y = $\frac{-9}{5}$

y = -1.8

Substitute the value of y in (1) to get

5x + y = -5

5x - 1.8 = -5

5x = - 5 + 1.8 = -3.2

x = $\frac{-3.2}{5}$

x = - 0.64

The solution for given system of equations are (x,y) = (-0.64, -1.8).