Question
4) \( \begin{array}{c}y=-6 x-1 \\ x+y=19\end{array} \)
Ask by Curry Wade. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -4 \) and \( y = 23 \).
Solution
To solve the system of equations:
\[
\begin{cases}
y = -6x - 1 \\
x + y = 19
\end{cases}
\]
**Step 1:** Substitute the expression for \( y \) from the first equation into the second equation.
\[
x + (-6x - 1) = 19
\]
**Step 2:** Simplify the equation.
\[
x - 6x - 1 = 19 \\
-5x - 1 = 19
\]
**Step 3:** Add 1 to both sides to isolate the term with \( x \).
\[
-5x = 20
\]
**Step 4:** Divide both sides by -5 to solve for \( x \).
\[
x = \frac{20}{-5} \\
x = -4
\]
**Step 5:** Substitute \( x = -4 \) back into the first equation to find \( y \).
\[
y = -6(-4) - 1 \\
y = 24 - 1 \\
y = 23
\]
**Solution:**
\[
x = -4 \quad \text{and} \quad y = 23
\]
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Simplify this solution Mind Expander
To solve these two equations, you can start by substituting the expression for \( y \) from the first equation into the second equation. So, replace \( y \) in the second equation with \( -6x - 1 \): \[ x + (-6x - 1) = 19 \] Now combine like terms: \[ -5x - 1 = 19 \] Add 1 to both sides: \[ -5x = 20 \] Now, divide by -5: \[ x = -4 \] Now that we have \( x \), we can substitute it back into the first equation to find \( y \): \[ y = -6(-4) - 1 = 24 - 1 = 23 \] Thus, the solution to the system of equations is \( x = -4 \) and \( y = 23 \). In other words, the coordinates of the intersection point are \( (-4, 23) \).
