The values of x and y that satisfy both equations are x = 2 and y = -6.
To solve the system of linear equations:
{2x+y=-2}
{5x+3y=-8}
We will use the method of substitution.
From the first equation, solve for y in terms of x: y = -2 - 2x
Substitute this value of y into the second equation: 5x + 3(-2 - 2x) = -8
Simplify and solve for x: 5x - 6 - 6x = -8
Combine like terms: -x - 6 = -8
Add 6 to both sides: -x = -2
Multiply both sides by -1: x = 2
Substitute this value of x back into the first equation to find y: 2(2) + y = -2
Solve for y: 4 + y = -2
Subtract 4 from both sides: y = -6
The values of x and y that satisfy both equations are x = 2 and y = -6.
The probable question may be:
"Consider the system of linear equations:
{2x+y=-2}
{5x+3y=-8}
Determine the values of \(x\) and \(y\) that satisfy both equations. Show all the steps of your solution process and state the final values for \(x\) and \(y\)."