Solve the system of equations.
8x−4y=−28
2x−6y=8
To solve the system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
First, solve one equation for one variable in terms of the other variable. We can rearrange the first equation to solve for x:
8x - 4y = -28
8x = 4y - 28
x = (4y - 28)/8
x = (y - 7)/2
Now substitute this expression for x into the second equation:
2x - 6y = 8
2((y - 7)/2) - 6y = 8
y - 7 - 6y = 8
-5y - 7 = 8
-5y = 8 + 7
-5y = 15
y = 15/(-5)
y = -3
Substitute the value of y back into the first equation to solve for x:
8x - 4(-3) = -28
8x + 12 = -28
8x = -28 - 12
8x = -40
x = -40/8
x = -5
Therefore, the solution to the system of equations is x = -5 and y = -3.
To solve this system of equations, we can use the method of substitution or elimination. I will show you how to solve it using the elimination method.
Step 1: Multiply the second equation by 4 to make the coefficients of 'y' in both equations equal.
4(2x - 6y) = 4(8)
8x - 24y = 32
Now, the system of equations becomes:
8x - 4y = -28
8x - 24y = 32
Step 2: Subtract the first equation from the second equation to eliminate 'x'.
(8x - 24y) - (8x - 4y) = 32 - (-28)
8x - 24y - 8x + 4y = 32 + 28
-20y = 60
Step 3: Divide both sides of the equation by -20 to solve for 'y'.
-20y / -20 = 60 / -20
y = -3
Step 4: Substitute the value of 'y' into one of the original equations to solve for 'x'.
8x - 4(-3) = -28
8x + 12 = -28
8x = -28 - 12
8x = -40
x = -40 / 8
x = -5
Step 5: Write the solution as an ordered pair (x, y).
The solution is (x, y) = (-5, -3).
To solve the system of equations, we'll use the method of substitution. Here's how you can do it:
Step 1: Solve one equation for one variable in terms of the other variable. In this case, let's solve the first equation for x:
8x - 4y = -28
We can rearrange this equation to solve for x:
8x = 4y - 28
Dividing both sides by 8, we get:
x = (4y - 28)/8
Step 2: Substitute the value of x obtained in step 1 into the other equation and solve for y. Let's substitute x into the second equation:
2x - 6y = 8
Substituting (4y - 28)/8 for x, we get:
2((4y - 28)/8) - 6y = 8
Simplifying, we have:
(4y - 28)/4 - 6y = 8
(4y - 28) - 24y = 32
-20y - 28 = 32
Step 3: Solve for y:
-20y = 32 + 28
-20y = 60
Dividing both sides by -20, we find:
y = -3
Step 4: Substitute the value of y back into either equation to solve for x. Let's use the first equation:
8x - 4(-3) = -28
8x + 12 = -28
8x = -28 - 12
8x = -40
Dividing both sides by 8, we get:
x = -5
So the solution to the system of equations is x = -5 and y = -3.