Question

1. -6x - 2y = -5

3x + y = -7

1. 3x - 5y = 7

x = 2y + 4

Explanation:

Step1: Solve the first - system of equations (-6x - 2y=-5, 3x + y=-7)

Multiply the second equation \(3x + y=-7\) by 2:
\[2(3x + y)=2\times(-7)\]
\[6x + 2y=-14\]
Add this new - equation to the first equation \(-6x - 2y=-5\):
\((-6x - 2y)+(6x + 2y)=-5+( - 14)\)
\[0=-19\]
This system has no solution since \(0
eq - 19\).

Step2: Solve the second - system of equations (3x - 5y = 7, x = 2y+4)

Substitute \(x = 2y + 4\) into the equation \(3x-5y = 7\):
\[3(2y + 4)-5y=7\]
Expand the left - hand side:
\[6y+12 - 5y=7\]
Combine like terms:
\[y+12 = 7\]
Subtract 12 from both sides:
\[y=7 - 12=-5\]
Substitute \(y=-5\) into \(x = 2y + 4\):
\[x=2\times(-5)+4=-10 + 4=-6\]

Answer:

The first system of equations \(-6x - 2y=-5\), \(3x + y=-7\) has no solution. The solution to the second system of equations \(3x - 5y = 7\), \(x = 2y+4\) is \(x=-6\), \(y = - 5\)