Question

The solution to the given system of equations is an ordered pair(x'y)
.


y=4-2/3x
4y+1=3x


Select a number for each blank to make each sentence true.

The x
-coordinate of the solution to the given system of equations is

. The y
-coordinate of the solution to the given systems of equations is

.

Answer 1

To solve the system of equations:

1. \( y = 4 - \frac{2}{3}x \)
2. \( 4y + 1 = 3x \)

We can start by substituting the expression for \( y \) from the first equation into the second equation.

Substituting \( y \) in the second equation:

\[
4(4 - \frac{2}{3}x) + 1 = 3x
\]

Now, distribute \( 4 \):

\[
16 - \frac{8}{3}x + 1 = 3x
\]

Combine the constant terms:

\[
17 - \frac{8}{3}x = 3x
\]

Next, let's rearrange the equation to isolate the terms involving \( x \):

Convert \( 3x \) to a fraction with a common denominator (3):

\[
17 = 3x + \frac{8}{3}x
\]

Express \( 3x \) as \( \frac{9}{3}x \):

\[
17 = \frac{9}{3}x + \frac{8}{3}x
\]

Now combine the fractions:

\[
17 = \frac{17}{3}x
\]

To isolate \( x \), multiply both sides by \( \frac{3}{17} \):

\[
x = 17 \cdot \frac{3}{17} = 3
\]

Now that we have \( x = 3 \), we can find \( y \) using the first equation:

\[
y = 4 - \frac{2}{3}(3)
\]

Calculating this gives:

\[
y = 4 - 2 = 2
\]

So the solution to the system of equations is:

\[
(x, y) = (3, 2)
\]

Now we can fill in the blanks:

The x-coordinate of the solution to the given system of equations is **3**. The y-coordinate of the solution to the given system of equations is **2**.