Question

Please help asap! thank you!

solve the system of equations:
6x / 5 + y / 15 = 2.3
x / 10 - 2y / 3 = 1.2
(the slashes represent fractions.)

Answer 1

To solve the system of equations, we can simplify both equations by dividing both sides by their respective denominators and rearrange them to isolate the x and y terms. Then, we can set the two expressions for x and y equal to each other, solve for one variable in terms of the other, and substitute that expression back into one of the original equations to solve for the other variable. The solution to the system of equations is x ≈ 0.598 and y ≈ 0.039.

Step-by-step explanation:

To solve the system of equations, we can start by simplifying both equations by dividing both sides of each equation by their respective denominators. For the first equation, we divide both sides by 5, and for the second equation, we divide both sides by 10. This gives us:

2x + (1/15)y = (23/10)x - (2/3)y = 1.2

Next, we can rearrange both equations so that the y terms are on one side and the x terms are on the other side. This gives us:

(23/10)x - 2x = (2/3)y - (1/15)y = 1.2

Finally, we can simplify both equations further and solve for x and y.

Let's start by simplifying the first equation:

(23/10)x - 2x = (23/10 - 20/10)x = (3/10)x

Now, let's simplify the second equation:

(2/3)y - (1/15)y = (2/3 - 1/15)y = (23/15)y

So, we have:

(3/10)x = (23/15)y = 1.2

Now, we can set the two expressions for x and y equal to each other:

(3/10)x = (23/15)y

From here, we can solve for x. To do this, we can multiply both sides of the equation by 10 and then divide both sides by 23/15:

x = (10/1) * (23/15)y = (230/15)y

Now, we can substitute this expression for x back into one of the original equations to solve for y. Let's use the first equation:

2x + (1/15)y = 1.2
2[(230/15)y] + (1/15)y = 1.2
(460/15)y + (1/15)y = 1.2
(461/15)y = 1.2
y = (1.2 * 15) / 461
y ≈ 0.039

Finally, we can substitute the value of y back into the expression for x to solve for x:

x = (230/15)y
x = (230/15) * 0.039
x ≈ 0.598

Therefore, the solution to the system of equations is x ≈ 0.598 and y ≈ 0.039.

Answer 2

The system of equations is solved by multiplying both equations to eliminate fractions, then using the elimination method to first solve for x, followed by substituting the value of x into one of the original equations to solve for y. The solution is x = 1.68 and y = -0.24.

Step-by-step explanation:

To solve the system of equations presented, let's first lay them out:

1.
`\((6x)/(5) + (y)/(15) = 2\)`
2
`. \((3x)/(10) - (2y)/(3) = 1.2\)`

We'll start by clearing the fractions to make the equations easier to manage. Multiply both sides of the first equation by 15, and both sides of the second equation by 10. Doing this results in:

1.
`\(18x + y = 30\)`

2.
`\(3x - 20y = 12\)`

Next, we will use the method of substitution or elimination to find the values of x and y. For this example, let's use elimination. We can multiply the first equation by 20 to align the coefficients of y:

1.
`\(360x + 20y = 600\)`
2.
`\(3x - 20y = 12\)`

Adding these two equations will cancel out y, giving us:

`\(363x = 612\)`

We can now solve for x:

`\(x = (612)/(363)\)`

After simplifying, we get:

`\(x = 1.68\)`

Now, we substitute x back into one of the original equations to find the value of y. Let’s use the first one:

`\(18(1.68) + y = 30\)`

Solving for y, we get:

`\(y = 30 - 18(1.68)\)`

`\(y = 30 - 30.24\)`

`\(y = -0.24\)`

So, the solution to the system of equations is
`\(x = 1.68\) and \(y = -0.24\).`