Solve the system of equations 2x+8y=8 and 2x-4y=-16
To solve the system of equations 2x + 8y = 8 and 2x - 4y = -16, we can proceed using the method of elimination.
First, let's multiply the second equation by 2 to make the coefficients of x in both equations the same:
2(2x - 4y) = 2(-16)
4x - 8y = -32
Now, we can subtract the first equation from the second equation to eliminate x:
(4x - 8y) - (2x + 8y) = -32 - 8
4x - 8y - 2x - 8y = -40
2x - 16y = -40
Now we have a new equation: 2x - 16y = -40
Let's multiply the first equation by 2 to make the coefficients of x the same in both equations:
2(2x + 8y) = 2(8)
4x + 16y = 16
Now, let's add the equations:
(4x + 16y) + (2x - 16y) = 16 - 40
4x + 16y + 2x - 16y = -24
6x = -24
Divide both sides of the equation by 6:
6x/6 = -24/6
x = -4
Now we can substitute this value of x into one of the original equations to solve for y. Let's use the first equation:
2x + 8y = 8
2(-4) + 8y = 8
-8 + 8y = 8
8y = 8 + 8
8y = 16
Divide both sides of the equation by 8:
8y/8 = 16/8
y = 2
So the solution to the system of equations 2x + 8y = 8 and 2x - 4y = -16 is x = -4 and y = 2.
To solve the system of equations 2x + 8y = 8 and 2x - 4y = -16, we will use the method of elimination.
Step 1: Multiply the second equation by 2 to make the coefficients of x in both equations equal:
2(2x - 4y) = 2(-16)
4x - 8y = -32
Step 2: Now we have the equations:
2x + 8y = 8
4x - 8y = -32
Add the two equations together:
(2x + 8y) + (4x - 8y) = 8 + (-32)
2x + 4x = -24
6x = -24
Step 3: Solve for x by dividing both sides of the equation by 6:
6x / 6 = -24 / 6
x = -4
Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
2(-4) + 8y = 8
-8 + 8y = 8
8y = 8 + 8
8y = 16
Step 5: Solve for y by dividing both sides of the equation by 8:
8y / 8 = 16 / 8
y = 2
Therefore, the solution to the system of equations 2x + 8y = 8 and 2x - 4y = -16 is x = -4 and y = 2.
To solve the system of equations 2x+8y=8 and 2x-4y=-16, we can use the method of substitution or elimination. Let's use the method of elimination.
Step 1: Multiply the second equation by -1 to eliminate the x term.
Original second equation: 2x - 4y = -16
Multiply both sides by -1: -2x + 4y = 16
Step 2: Add the two equations together to eliminate the x term.
(2x + 8y) + (-2x + 4y) = 8 + 16
Simplify: 12y = 24
Step 3: Solve for y.
Divide both sides by 12: y = 2
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Let's use the first equation: 2x + 8y = 8
Substitute y = 2: 2x + 8(2) = 8
Simplify: 2x + 16 = 8
Subtract 16 from both sides: 2x = -8
Divide both sides by 2: x = -4
Therefore, the solution to the system of equations is x = -4 and y = 2.