Question

Solve for X and y using any method. 0.0 5X plus Y equals four. X over 2+ Y over three equals 4/3

Answer 1

It’s not 5X for the first equation. It’s 0.05x

Answer 2

It’s not 5X for the first equation. It’s0.05x

Answer 3

To solve the system of equations given by

1. \( 5X + Y = 4 \)
2. \( \frac{X}{2} + \frac{Y}{3} = \frac{4}{3} \)

we can use the substitution or elimination method. Let's first simplify the second equation.

### Step 1: Eliminate the fractions in equation 2.

Multiply both sides of the second equation by 6 (the least common multiple of 2 and 3) to eliminate the fractions:

\[
6\left(\frac{X}{2}\right) + 6\left(\frac{Y}{3}\right) = 6\left(\frac{4}{3}\right)
\]

This simplifies to:

\[
3X + 2Y = 8
\]

Now we have the system:

1. \( 5X + Y = 4 \) (Equation 1)
2. \( 3X + 2Y = 8 \) (Equation 2)

### Step 2: Solve for Y in terms of X using Equation 1.

From Equation 1:

\[
Y = 4 - 5X
\]

### Step 3: Substitute Y in Equation 2.

Now substitute \( Y \) in Equation 2:

\[
3X + 2(4 - 5X) = 8
\]

Distributing the 2:

\[
3X + 8 - 10X = 8
\]

Combine like terms:

\[
-7X + 8 = 8
\]

Subtract 8 from both sides:

\[
-7X = 0
\]

Divide both sides by -7:

\[
X = 0
\]

### Step 4: Substitute X back into the equation for Y.

Now substitute \( X = 0 \) back into the equation \( Y = 4 - 5X \):

\[
Y = 4 - 5(0) = 4
\]

### Step 5: Solution

Thus, the solution to the system is:

\[
X = 0, \quad Y = 4
\]

### Final Answer
\[
(X, Y) = (0, 4)
\]

Answer 4

Thank you for your clarification! Let's solve the equations with the correct coefficient for \(X\).

We have the following system of equations:

1. \( 0.05X + Y = 4 \)
2. \( \frac{X}{2} + \frac{Y}{3} = \frac{4}{3} \)

### Step 1: Solve the first equation for \(Y\)

From equation 1:

\[
Y = 4 - 0.05X
\]

### Step 2: Substitute \(Y\) in the second equation

Substitute \(Y\) into equation 2:

\[
\frac{X}{2} + \frac{4 - 0.05X}{3} = \frac{4}{3}
\]

Now, let's eliminate the fractions by multiplying every term by 6 (the least common multiple of 2 and 3):

\[
6\left(\frac{X}{2}\right) + 6\left(\frac{4 - 0.05X}{3}\right) = 6\left(\frac{4}{3}\right)
\]

This simplifies to:

\[
3X + 2(4 - 0.05X) = 8
\]

Now distribute the 2:

\[
3X + 8 - 0.1X = 8
\]

### Step 3: Combine like terms

Combine \(3X\) and \(-0.1X\):

\[
(3 - 0.1)X + 8 = 8
\]

This simplifies to:

\[
2.9X + 8 = 8
\]

### Step 4: Solve for \(X\)

Subtract 8 from both sides:

\[
2.9X = 0
\]

Divide by 2.9:

\[
X = 0
\]

### Step 5: Substitute \(X\) back to find \(Y\)

Substitute \(X = 0\) back into the equation for \(Y\):

\[
Y = 4 - 0.05(0) = 4
\]

### Final Answer

So the solution is:

\[
(X, Y) = (0, 4)
\]

Answer 5

Thank you for your patience! Let's solve the equations using the correct coefficients:

We have the following system of equations:

1. \( 0.05X + Y = 4 \)
2. \( \frac{X}{2} + \frac{Y}{3} = \frac{4}{3} \)

### Step 1: Solve the first equation for \(Y\)

From the first equation:

\[
Y = 4 - 0.05X
\]

### Step 2: Substitute \(Y\) into the second equation

Substituting \(Y\) into the second equation gives:

\[
\frac{X}{2} + \frac{4 - 0.05X}{3} = \frac{4}{3}
\]

### Step 3: Clear the fractions

To eliminate the fractions, multiply the entire equation by 6 (the least common multiple of 2 and 3):

\[
6\left(\frac{X}{2}\right) + 6\left(\frac{4 - 0.05X}{3}\right) = 6\left(\frac{4}{3}\right)
\]

This simplifies to:

\[
3X + 2(4 - 0.05X) = 8
\]

### Step 4: Distribute and combine like terms

Distributing the 2:

\[
3X + 8 - 0.1X = 8
\]

Combine \(3X\) and \(-0.1X\):

\[
(3 - 0.1)X + 8 = 8
\]

This becomes:

\[
2.9X + 8 = 8
\]

### Step 5: Solve for \(X\)

Subtract 8 from both sides:

\[
2.9X = 0
\]

Divide by 2.9:

\[
X = 0
\]

### Step 6: Substitute \(X\) back to find \(Y\)

Now substitute \(X = 0\) back into the equation for \(Y\):

\[
Y = 4 - 0.05(0) = 4
\]

### Final Answer

Thus, the solution to the system of equations is:

\[
(X, Y) = (0, 4)
\]

Thank you for your understanding, and please let me know if you have any further questions!