Solve the system by substitution.
x + 3y = -4
2x + 2y = -8
x + 3 y = - 4 Multiply both sides by 2
2 x + 6 y = - 8
2 x + 6 y = - 8
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2 x + 2 y = - 8
_____________________
- 4 y = 0
y = 0
x + 3 y = - 4
x + 3 * 0 = - 4
x + 0 = - 4
x = - 4
Te solutions are :
x = - 4 , y = 0
Nice job using elimination. For substitution, though, note that
x = -4-3y
so, substituting that into the other equation, we have
2x+2y = -8
2(-4-3y)+2y = -8
-8-6y+2y = -8
-4y = 0
y=0
so, x=-4-3y = -4
as found above
To solve the system of equations by substitution, we will start by solving one equation for one variable and then substitute this expression into the other equation.
Let's solve the first equation, x + 3y = -4, for x. Subtract 3y from both sides to isolate x:
x = -4 - 3y
Now, substitute this expression for x into the second equation, 2x + 2y = -8:
2(-4 - 3y) + 2y = -8
Simplify the equation by distributing the 2:
-8 - 6y + 2y = -8
Combine like terms:
-4y - 8 = -8
Add 8 to both sides:
-4y = 0
Divide both sides by -4:
y = 0
Now that we have found the value of y, substitute it back into the first equation to find the value of x:
x + 3(0) = -4
x = -4
Therefore, the solution to the system of equations is x = -4 and y = 0.
To solve the system of equations by substitution, we need to isolate one variable in one equation and substitute that expression into the other equation.
Let's solve the first equation for x:
x + 3y = -4
x = -4 - 3y
Now, substitute the expression for x into the second equation:
2x + 2y = -8
2(-4 - 3y) + 2y = -8
Simplify the equation:
-8 - 6y + 2y = -8
-8 - 4y = -8
Now, we can solve for y:
-4y = 0
y = 0
Next, substitute the value of y back into the first equation to solve for x:
x + 3(0) = -4
x + 0 = -4
x = -4
Therefore, the solution to the system of equations is x = -4 and y = 0.