Solve the system of equations.

2x+3y=19                                    4x−5y=5

To solve the system of equations:

1. \(2x + 3y = 19\)
2. \(4x - 5y = 5\)

We can use the method of elimination or substitution. Here, I'll use the elimination method:

1. Multiply the first equation by 2 to align the coefficients of \(x\):

\[
4x + 6y = 38
\]

2. Now we have the modified system:

\[
4x + 6y = 38 \quad \text{(Equation 3)}
\]
\[
4x - 5y = 5 \quad \text{(Equation 2)}
\]

3. Subtract Equation 2 from Equation 3:

\[
(4x + 6y) - (4x - 5y) = 38 - 5
\]

\[
4x + 6y - 4x + 5y = 33
\]

\[
11y = 33
\]

\[
y = \frac{33}{11} = 3
\]

4. Substitute \(y = 3\) back into the first original equation to solve for \(x\):

\[
2x + 3(3) = 19
\]

\[
2x + 9 = 19
\]

\[
2x = 19 - 9
\]

\[
2x = 10
\]

\[
x = \frac{10}{2} = 5
\]

Thus, the solution to the system of equations is:

\[
x = 5, \quad y = 3
\]

Would you like details or have any questions?

Here are 5 more math-related questions you might be interested in:

1. How do you solve a quadratic equation using the quadratic formula?
2. Can you explain the Pythagorean theorem with an example?
3. How do you find the derivative of a function using the power rule?
4. What is the process for solving a system of linear equations using matrix methods?
5. How do you integrate a function using substitution?

**Tip:** When solving systems of equations, aligning coefficients for elimination can simplify the process of finding the solution.

Learn how to solve the system of equations 2x + 3y = 19 and 4x - 5y = 5 using the elimination method with a detailed step-by-step solution. Suitable for students in Grades 9-12.

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