Final answer:
To solve the system of linear equations by substitution, isolate y in the second equation to get y = -3 - x, substitute this into the first equation, solve for x to find x = 5, and then substitute x back into the isolated equation to find y = -8.
Step-by-step explanation:
To solve the system of linear equations 5x + 2y = 9 and x + y = -3 by substitution, we can start by expressing one variable in terms of another. From the second equation, we can isolate y by subtracting x from both sides, yielding y = -3 - x. Next, we substitute this expression for y into the first equation.
So the first equation becomes 5x + 2(-3 - x) = 9. Simplifying this, we get 5x - 6 - 2x = 9, which further simplifies to 3x - 6 = 9. Adding 6 to both sides gives us 3x = 15, and dividing by 3 yields x = 5.
Now, we substitute x = 5 back into the equation y = -3 - x to find the value of y. This gives us y = -3 - 5, which simplifies to y = -8.
Therefore, the solution to the system of equations is x = 5 and y = -8.