Question

Use substitution to solve this system of equations .y 1 3x 5 24 y 5 x 1 4 The second equation tells you Now you can find the value of y . that y 5 x 1 4, so you can substitute You can substitute 22 for x into x 1 4 for y in the first equation and either equation and solve for y . solve for x . Try using the second equation .y 1 3x 5 24 y 5 x 1 4 (x 1 4) 1 3x 5 24 4x 1 4 5 24 y 5 22 1 4 4x 5 28 y 5 2 x 5 22The solution is (22, 2) Once you know the value of one variable in a system of equations, how can you find the value of the second variable

Answer 1

To solve the system of equations using substitution, as you've started to demonstrate, let's go through the steps clearly.

You have the following system of equations:

1) \( y + 3x = 24 \)
2) \( y = x + 4 \)

From the second equation, you can express \( y \) in terms of \( x \):
\[
y = x + 4
\]

Now, you can substitute this expression for \( y \) into the first equation:

\[
(x + 4) + 3x = 24
\]

Combining like terms:
\[
x + 4 + 3x = 24
\]
\[
4x + 4 = 24
\]

Now, subtract 4 from both sides:
\[
4x = 20
\]

Next, divide by 4:
\[
x = 5
\]

Now that we have the value of \( x \), we can find the value of \( y \) using the second equation:

\[
y = x + 4
\]
Substituting \( x = 5 \):
\[
y = 5 + 4 = 9
\]

So the solution to the system of equations is:
\[
(x, y) = (5, 9)
\]

### Answering your question
Once you find the value of one variable in a system of equations, you can find the value of the second variable by substituting the known value back into one of the original equations. This allows you to solve for the second variable directly.