Use substitution to solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

[tex]\[ \begin{cases}
3x + 4y = 9 \\
y = 2 - x
\end{cases} \][/tex]



Answer :

Certainly! Let's solve the system of equations using the substitution method. The given system of equations is:

[tex]\[ \begin{cases} 3x + 4y = 9 \\ y = 2 - x \end{cases} \][/tex]

First, we'll substitute the second equation, [tex]\( y = 2 - x \)[/tex], into the first equation.

1. Substitute [tex]\( y = 2 - x \)[/tex] into [tex]\( 3x + 4y = 9 \)[/tex]:

[tex]\[ 3x + 4(2 - x) = 9 \][/tex]

2. Distribute the 4 in the equation:

[tex]\[ 3x + 8 - 4x = 9 \][/tex]

3. Combine like terms:

[tex]\[ 3x - 4x + 8 = 9 \\ -x + 8 = 9 \][/tex]

4. Solve for [tex]\( x \)[/tex]:

[tex]\[ -x = 9 - 8 \\ -x = 1 \\ x = -1 \][/tex]

Now that we have [tex]\( x = -1 \)[/tex], we substitute this value back into the second equation to find [tex]\( y \)[/tex]:

5. Substitute [tex]\( x = -1 \)[/tex] into [tex]\( y = 2 - x \)[/tex]:

[tex]\[ y = 2 - (-1) \\ y = 2 + 1 \\ y = 3 \][/tex]

So, the solution to the system of equations is:

[tex]\[ (x, y) = (-1, 3) \][/tex]