What is the solution of the system use substitution
x=-2y+10
-6y=6x-6
Z=-3x+10y
To solve the system using substitution, we'll solve one of the equations for one variable and substitute it into the other equations.
From the first equation x = -2y + 10, we can rearrange it to solve for y:
x = -2y + 10
2y = -x + 10
y = (-x + 10)/2
y = -0.5x + 5
Now we substitute this value of y into the second equation:
-6y = 6x - 6
-6(-0.5x + 5) = 6x - 6
3x - 30 = 6x - 6
-3x = 24
x = -8
Now substitute this value of x into the equation Z = -3x + 10y:
Z = -3(-8) + 10y
Z = 24 + 10y
Z = 10y + 24
So the solution of the system is:
x = -8
y = -0.5x + 5 = -0.5(-8) + 5 = 9
Z = 10y + 24 = 10(9) + 24 = 114
To solve the system of equations using substitution, we need to solve one equation for a variable and substitute it into the other equations. Let's start with the first equation:
Equation 1: x = -2y + 10
We can solve this equation for x by expressing it in terms of y:
x = -2y + 10
Next, let's substitute this expression for x in the other two equations.
Equation 2: -6y = 6x - 6
Substituting the expression for x:
-6y = 6(-2y + 10) - 6
Simplifying the equation:
-6y = -12y + 60 - 6
-6y + 12y = 60 - 6
6y = 54
Divide both sides of the equation by 6:
y = 9
Now, substitute the value of y into Equation 1 to find the value of x:
x = -2(9) + 10
x = -18 + 10
x = -8
Finally, let's substitute the values of x and y into the third equation:
z = -3x + 10y
z = -3(-8) + 10(9)
z = 24 + 90
z = 114
Therefore, the solution to the given system of equations is:
x = -8, y = 9, z = 114.
To find the solution to the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equations.
First, let's solve the first equation, x = -2y + 10, for x in terms of y:
x = -2y + 10
Next, we substitute this expression for x into the second equation, -6y = 6x - 6:
-6y = 6(-2y + 10) - 6
Now, let's simplify the equation:
-6y = -12y + 60 - 6
-6y = -12y + 54
Next, add 12y to both sides of the equation to eliminate the negative sign:
-6y + 12y = -12y + 12y + 54
6y = 54
Next, divide both sides of the equation by 6 to isolate y:
(6y) / 6 = 54 / 6
y = 9
Now that we have the value of y, we can substitute it back into the first equation to find x:
x = -2(9) + 10
x = -18 + 10
x = -8
Therefore, the solution to the system of equations is x = -8 and y = 9.