Question
\( \left\{ \begin{array} { l } { y = - 6 } \\ { x = - 4 y - 5 } \end{array} \left\{ \begin{array} { l } { x = \square } \end{array} \right. \right. \)
Ask by Boyd Horton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 19 \)
Solution
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}y=-6\\x=-4y-5\end{array}\right.\)
- step1: Substitute the value of \(y:\)
\(x=-4\left(-6\right)-5\)
- step2: Simplify:
\(x=19\)
- step3: Calculate:
\(\left\{ \begin{array}{l}x=19\\y=-6\end{array}\right.\)
- step4: Check the solution:
\(\left\{ \begin{array}{l}x=19\\y=-6\end{array}\right.\)
- step5: Rewrite:
\(\left(x,y\right) = \left(19,-6\right)\)
To solve the system of equations:
1. **First Equation:** \( y = -6 \)
2. **Second Equation:** \( x = -4y - 5 \)
We can substitute the value of \( y \) from the first equation into the second equation.
### Step 1: Substitute \( y \)
Substituting \( y = -6 \) into the second equation:
\[
x = -4(-6) - 5
\]
### Step 2: Calculate \( x \)
Now, calculate \( x \):
\[
x = 24 - 5 = 19
\]
### Final Solution
Thus, the solution to the system of equations is:
\[
(x, y) = (19, -6)
\]
So, \( x = 19 \) and \( y = -6 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve this system, we can start with the first equation, where \( y = -6 \). Now, substitute this value back into the second equation: \[ x = -4(-6) - 5 \] Calculating this gives: \[ x = 24 - 5 = 19 \] So, we find that \( x = 19 \). Therefore, the solution to the system is \( (x, y) = (19, -6) \). If you take the time to graph these equations, you'll see that the line \( y = -6 \) is a horizontal line, and the line described by \( x = -4y - 5 \) will intersect it at the point we calculated. It’s a fun way to visualize the solution!
