Final answer:
To solve the equations 7x+2y=-19 and -x+2y=21 by substitution, we first solved the second equation for x, and then substituted this expression into the first equation to find y. After finding y, we substituted it back into the expression for x to find its value. The solution is x = -5 and y = 8.
Step-by-step explanation:
To solve the system of equations 7x+2y=-19 and -x+2y=21 by substitution, we start by solving one of the equations for one variable and then substituting that expression into the other equation. Let's solve the second equation for x:
-x + 2y = 21
-x = 21 - 2y
x = -21 + 2y
Now, substitute x in the first equation with the expression we found:
7(-21 + 2y) + 2y = -19
-147 + 14y + 2y = -19
16y = 128
y = 8
With the value of y found, substitute it back into the expression for x:
x = -21 + 2(8)
x = -21 + 16
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 8.