Solve each system by using the elimination method. Make sure to write your answer in (x,y) form.

0.2x - 0.5y = -27.8
0.3x + 0.4y = 68.7

First, I would get rid of the decimals. It will make life easier. So, multiply both sides of each equation by 10.

(That is perfectly legal as long as you do it to both sides of an equation).

2x - 5y = -278
3x + 4y = 687

Our goal is to eliminate either the x or the y.

Since the y's have opposite signs, you might decide it is easier to eliminate y.
To eliminate the y's you will need a -20 and +20 (since 4 times 5 = 20)

Multiply the first equation by 4 and the 2nd equation by 5.

Now, add the coefficients for the x term and add the constants on the other side of the equal sign.

Solve for x by dividing both sides by the coefficient of x.

You now, have the value for x. Substitute that value for x into one of the original equations and solve for y.

Be sure to check in both equations to be sure you haven't made a mistake.

I will be happy to check your final answers or help more along the way if you need additional help.

To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations.

Let's begin by eliminating the variable y.

We can do this by multiplying the first equation by 2 and the second equation by 5 to make the coefficients of y the same.

So, multiplying the first equation by 2:
2(0.2x - 0.5y) = 2(-27.8)
0.4x - y = -55.6

And multiplying the second equation by 5:
5(0.3x + 0.4y) = 5(68.7)
1.5x + 2y = 343.5

Now we have:
0.4x - y = -55.6 ----(1)
1.5x + 2y = 343.5 ----(2)

To eliminate y, we can add these equations together:

(0.4x - y) + (1.5x + 2y) = -55.6 + 343.5

Combining like terms:
1.9x + y = 287.9 ----(3)

Now we have two equations:
0.4x - y = -55.6 ----(1)
1.9x + y = 287.9 ----(3)

We can now solve this system by either substitution or adding the equations.

For simplicity, let's add the equations to eliminate y.

(0.4x - y) + (1.9x + y) = -55.6 + 287.9

Combining like terms:
2.3x = 232.3

Divide both sides by 2.3 to solve for x:
x = 232.3 / 2.3
x = 101

Now substitute the value of x into equation (3) to find the value of y:

1.9(101) + y = 287.9

191.9 + y = 287.9

Subtract 191.9 from both sides:
y = 287.9 - 191.9
y = 96

Therefore, the solution to the system of equations is (x, y) = (101, 96).

To solve this system of equations using the elimination method, the goal is to eliminate one variable by adding or subtracting the two equations.

First, we need to manipulate the equations so that when we add or subtract them, one of the variables will cancel out.

Let's start by multiplying both sides of the first equation by 10 to get rid of decimals:

(10)(0.2x - 0.5y) = (10)(-27.8)
2x - 5y = -278

Now, let's multiply both sides of the second equation by 10:

(10)(0.3x + 0.4y) = (10)(68.7)
3x + 4y = 687

Now we have:

2x - 5y = -278
3x + 4y = 687

Next, we will multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations equal:

(3)(2x - 5y) = (3)(-278)
6x - 15y = -834

(2)(3x + 4y) = (2)(687)
6x + 8y = 1374

Now we have:

6x - 15y = -834
6x + 8y = 1374

We can eliminate x by subtracting the first equation from the second equation:

(6x + 8y) - (6x - 15y) = 1374 - (-834)
6x + 8y - 6x + 15y = 1374 + 834
23y = 2208

Divide both sides of the equation by 23:
y = 2208 / 23
y ≈ 96

Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

0.2x - 0.5y = -27.8

0.2x - 0.5(96) = -27.8
0.2x - 48 = -27.8

Add 48 to both sides of the equation:

0.2x = 20.2

Divide both sides of the equation by 0.2:

x = 20.2 / 0.2
x = 101

Therefore, the solution to the system of equations is (x, y) = (101, 96).