-5x+2y=15
x-3y= -16
Use substitution to solve the system.
by the 2nd equation, x = 3y-16
so substitute that into the 1st equation, and you have
-5(3y-16)+2y = 15
y = 5
so x = -1
To solve the system of equations using substitution, we will solve one equation for one variable and substitute it into the other equation.
Let's solve the second equation for x:
x - 3y = -16
x = 3y - 16
Now, substitute this value of x into the first equation:
-5(3y - 16) + 2y = 15
-15y + 80 + 2y = 15
-13y + 80 = 15
-13y = 15 - 80
-13y = -65
y = -65 / -13
y = 5
Now substitute the value of y back into the second equation to find x:
x = 3(5) - 16
x = 15 - 16
x = -1
Therefore, the solution to the system of equations is x = -1 and y = 5.
To solve the system of equations using substitution, we need to isolate a variable in one equation and substitute this expression into the other equation. Let's start by isolating x in the second equation.
x - 3y = -16
Add 3y to both sides to isolate x:
x = -16 + 3y
Now we have an expression for x in terms of y. We can substitute this expression into the first equation:
-5x + 2y = 15
Replace x with -16 + 3y:
-5(-16 + 3y) + 2y = 15
Distribute -5:
80 - 15y + 2y = 15
Combine like terms:
-15y + 2y = 15 - 80
-13y = -65
Divide both sides by -13 to solve for y:
y = -65 / -13
y = 5
Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the second equation:
x - 3y = -16
Replace y with 5:
x - 3(5) = -16
x - 15 = -16
Add 15 to both sides to solve for x:
x = -16 + 15
x = -1
Therefore, the solution to the system of equations is x = -1 and y = 5.