Question

system of equations
you have been experimenting with two representations of the following system of equations:
2x + 3 = y
2x + y = 15
a solution to a system of equations is a set of values that makes both equations in that system true.
write the solution to this system as an ordered pair.
( , )
submit and explain
(there are also two hanger diagrams: hanger a with 2x + 3 = y (showing two x - shaped weights, one 3 - lb weight on one side and one y - shaped weight on the other) and hanger b with 2x + y = 15 (showing two x - shaped weights, one y - shaped weight on one side and five 3 - lb weights on the other))

Explanation:

Step1: Substitute \( y = 2x + 3 \) into the second equation

We have the system:
\[

$$\begin{cases} 2x + 3 = y \\ 2x + y = 15 \end{cases}$$

\]
Substitute \( y \) from the first equation into the second: \( 2x + (2x + 3) = 15 \)

Step2: Simplify and solve for \( x \)

Simplify the left - hand side: \( 2x+2x + 3=15 \), which combines to \( 4x+3 = 15 \)
Subtract 3 from both sides: \( 4x=15 - 3=12 \)
Divide both sides by 4: \( x=\frac{12}{4}=3 \)

Step3: Solve for \( y \)

Substitute \( x = 3 \) into the first equation \( y=2x + 3 \)
\( y=2\times3+3=6 + 3=9 \)

Answer:

\((3,9)\)