Of course, let's solve the given system of simultaneous equations step-by-step:
Given the system of equations:
[tex]\[
\begin{cases}
1. & x + y = 7 \\
2. & 2x + 3y = 4
\end{cases}
\][/tex]
1. Solve the first equation for [tex]\( y \)[/tex]:
[tex]\[
x + y = 7 \implies y = 7 - x
\][/tex]
2. Substitute [tex]\( y = 7 - x \)[/tex] into the second equation:
[tex]\[
2x + 3(7 - x) = 4
\][/tex]
3. Expand and simplify the second equation:
[tex]\[
2x + 21 - 3x = 4
\][/tex]
[tex]\[
2x - 3x + 21 = 4
\][/tex]
[tex]\[
-x + 21 = 4
\][/tex]
4. Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
-x + 21 = 4 \implies -x = 4 - 21 \implies -x = -17 \implies x = 17
\][/tex]
5. Substitute [tex]\( x = 17 \)[/tex] back into the equation [tex]\( y = 7 - x \)[/tex] to find [tex]\( y \)[/tex]:
[tex]\[
y = 7 - 17
\][/tex]
[tex]\[
y = -10
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
x = 17 \quad \text{and} \quad y = -10
\][/tex]
So, the values are [tex]\( x = 17 \)[/tex] and [tex]\( y = -10 \)[/tex].
