Certainly! Let's solve each system of equations step-by-step.
System 1:
[tex]\[
\left\{
\begin{array}{lr}
2x - 5y = 11 & \\
3x - 4y = 6 & y = -3
\end{array}
\right.
\][/tex]
We are given that [tex]\( y = -3 \)[/tex]. We can substitute [tex]\( y \)[/tex] into both equations to find [tex]\( x \)[/tex].
1. Substituting [tex]\( y = -3 \)[/tex] into the first equation:
[tex]\[
2x - 5(-3) = 11 \\
2x + 15 = 11 \\
2x = 11 - 15 \\
2x = -4 \\
x = -2
\][/tex]
So, the solutions for the first system are [tex]\( x = -2 \)[/tex] and [tex]\( y = -3 \)[/tex].
System 2:
[tex]\[
\left\{
\begin{array}{lr}
5x - 3y = 0 & \\
7x - y = -16 & y = -5
\end{array}
\right.
\][/tex]
We are given that [tex]\( y = -5 \)[/tex]. We can substitute [tex]\( y \)[/tex] into both equations to find [tex]\( x \)[/tex].
1. Substituting [tex]\( y = -5 \)[/tex] into the first equation:
[tex]\[
5x - 3(-5) = 0 \\
5x + 15 = 0 \\
5x = -15 \\
x = -3
\][/tex]
So, the solutions for the second system are [tex]\( x = -3 \)[/tex] and [tex]\( y = -5 \)[/tex].
To summarize:
- For the first system of equations: [tex]\(\{2x - 5y = 11\)[/tex], [tex]\(3x - 4y = 6\}\)[/tex], the solution is [tex]\( x = -2 \)[/tex] and [tex]\( y = -3 \)[/tex].
- For the second system of equations: [tex]\(\{5x - 3y = 0\)[/tex], [tex]\(7x - y = -16\}\)[/tex], the solution is [tex]\( x = -3 \)[/tex] and [tex]\( y = -5 \)[/tex].
