Solve the system of two equations using substitution.y=2+3x 4x−3y=−16
We have the two equations:
1) y = 2 + 3x
2) 4x - 3y = -16
We can start by solving equation 1) for y. Rearranging the equation, we get:
y = 3x + 2
Now we substitute this expression for y into equation 2). We have:
4x - 3(3x + 2) = -16
Expanding the expression:
4x - 9x - 6 = -16
Combining like terms:
-5x - 6 = -16
Now, let's isolate x. Adding 6 to both sides:
-5x = -10
Dividing by -5:
x = 2
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 3(2) + 2
y = 6 + 2
y = 8
Therefore, the solution to the system of equations is x = 2 and y = 8.
To solve the system of equations using substitution, we will solve one equation for one variable and then substitute it into the other equation.
Let's start with the first equation:
y = 2 + 3x
We can solve this equation for y by subtracting 2 from both sides:
y - 2 = 3x
Next, let's solve the second equation:
4x - 3y = -16
Now, substitute the value of y from the first equation into the second equation:
4x - 3(2 + 3x) = -16
Distribute the -3:
4x - 6 - 9x = -16
Combine like terms:
-5x - 6 = -16
Now, add 6 to both sides:
-5x = -10
Divide both sides by -5:
x = 2
Now that we have the value of x, we can substitute it back into the first equation to find the value of y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is x = 2 and y = 8.
To solve this system of equations using substitution, we need to isolate one variable in either equation and substitute it into the other equation. Let's start by isolating y in the first equation:
y = 2 + 3x
Now, let's substitute this value of y into the second equation:
4x - 3(2 + 3x) = -16
First, distribute the -3:
4x - 6 - 9x = -16
Combine like terms:
-5x - 6 = -16
Add 6 to both sides:
-5x = -10
Divide both sides by -5:
x = 2
Now that we have the value of x, we can substitute it back into the first equation to find y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is x = 2 and y = 8.