Question

solve by substitution.\

$$\begin{cases}-3x + y = 19\\\\2x - 3y = -1\\end{cases}$$

\\((?,\\ \\ \\ \\ \\ )\\)

Explanation:

Step1: Solve for y from the first equation

From \(-3x + y = 19\), we can express \(y\) in terms of \(x\) by adding \(3x\) to both sides. So, \(y = 3x + 19\).

Step2: Substitute y into the second equation

Substitute \(y = 3x + 19\) into \(2x - 3y = -1\). We get \(2x - 3(3x + 19) = -1\).

Step3: Simplify and solve for x

First, expand the left - hand side: \(2x-9x - 57=-1\).
Combine like terms: \(-7x-57 = - 1\).
Add 57 to both sides: \(-7x=-1 + 57\), which simplifies to \(-7x = 56\).
Divide both sides by \(-7\): \(x=\frac{56}{-7}=-8\).

Step4: Substitute x back to find y

Substitute \(x = - 8\) into \(y = 3x+19\). Then \(y=3\times(-8)+19=-24 + 19=-5\).

Answer:

\((-8,-5)\)