Certainly! Let's solve the given system of linear equations to identify the ordered pair that satisfies both equations.
The system is:
[tex]\[
\begin{cases}
x + 4y = 3 \\
y = -4x - 3
\end{cases}
\][/tex]
We can solve this system by substitution or elimination, but since the second equation already expresses [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], substitution is convenient.
### Step 1: Substitute [tex]\( y = -4x - 3 \)[/tex] into [tex]\( x + 4y = 3 \)[/tex]
[tex]\[
x + 4(-4x - 3) = 3
\][/tex]
### Step 2: Simplify the equation
[tex]\[
x + 4(-4x) + 4(-3) = 3
\][/tex]
[tex]\[
x - 16x - 12 = 3
\][/tex]
[tex]\[
-15x - 12 = 3
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
[tex]\[
-15x = 3 + 12
\][/tex]
[tex]\[
-15x = 15
\][/tex]
[tex]\[
x = \frac{15}{-15}
\][/tex]
[tex]\[
x = -1
\][/tex]
### Step 4: Substitute [tex]\( x = -1 \)[/tex] back into [tex]\( y = -4x - 3 \)[/tex] to find [tex]\( y \)[/tex]
[tex]\[
y = -4(-1) - 3
\][/tex]
[tex]\[
y = 4 - 3
\][/tex]
[tex]\[
y = 1
\][/tex]
Thus, [tex]\( x = -1 \)[/tex] and [tex]\( y = 1 \)[/tex]. The ordered pair that is a solution to the system is [tex]\( (-1, 1) \)[/tex].
### Verification
To ensure our solution is correct, let's substitute [tex]\( (-1, 1) \)[/tex] back into both original equations:
1. Check [tex]\( x + 4y = 3 \)[/tex]:
[tex]\[
-1 + 4(1) = -1 + 4 = 3
\][/tex]
2. Check [tex]\( y = -4x - 3 \)[/tex]:
[tex]\[
1 = -4(-1) - 3 = 4 - 3 = 1
\][/tex]
Both equations are satisfied with [tex]\( (-1, 1) \)[/tex].
### Conclusion
The ordered pair that is a solution to the system of linear equations is:
[tex]\[
(-1, 1)
\][/tex]
