y=3x+2
4x-2y=-8
Solve using Elimination method
perfectly set up for using substitution:
in the 2nd:
4x - 2(3x+2) = -8
4x - 6x - 4 = -8
-2x = -4
x = 2 , then y = 3(2) + 2 = 8
but, anyway...
line them up in a better way:
#1: 3x - y = -2
#2: 4x - 2y = -8
double the first:
6x - 2y = -4
subtract the 2nd:
2x = 4
x = 2
sub back into the 1st:
3x - y = -2
3(2) - y = -2
6 - y = -2
-y = -8
y = 8
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply the first equation by 2 to make the coefficients of y in both equations equal.
2*(y = 3x+2) => 2y = 6x + 4
Now the first equation becomes: 2y = 6x + 4
Step 2: Rewrite the second equation.
4x - 2y = -8
Step 3: Add the two equations together.
(2y = 6x + 4) + (4x - 2y = -8)
Simplifying, we get:
6x + 4x = -8 + 4
10x = -4
Step 4: Divide both sides by 10 to solve for x.
x = -4/10
Simplifying, we get:
x = -2/5
Step 5: Substitute the value of x back into either of the original equations to solve for y.
Using the first equation:
y = 3x + 2
y = 3*(-2/5) + 2
y = -6/5 + 2
y = -6/5 + 10/5
y = 4/5
So the solution to the system of equations is x = -2/5 and y = 4/5.
To solve the system of equations using the elimination method, we'll eliminate one variable by adding or subtracting the equations.
The given system of equations is:
y = 3x + 2 ...(Equation 1)
4x - 2y = -8 ...(Equation 2)
Step 1: Multiply both sides of Equation 1 by 2 to make the coefficients of 'y' equal in both equations:
2y = 6x + 4 ...(Equation 3)
Step 2: Add Equation 2 and Equation 3 to eliminate the 'y' variable:
(4x - 2y) + (2y) = -8 + (6x + 4)
Simplifying the equation:
4x - 2y + 2y = -8 + 6x + 4
4x = 6x - 4
Step 3: Rearrange the equation by moving all the terms containing 'x' to the left side and all the constant terms to the right side:
4x - 6x = -4
-2x = -4
Step 4: Solve for 'x' by dividing both sides of the equation by -2:
x = (-4) / (-2)
x = 2
Step 5: Substitute the value of 'x' back into Equation 1 to find the value of 'y':
y = 3(2) + 2
y = 6 + 2
y = 8
So, the solution to the given system of equations is x = 2 and y = 8.