Given the system
\[
\begin{array}{l}
10 x+3 y=-19 \\
9 x+5 y=-1
\end{array}
\]
what is the point of intersection?
\[
\begin{array}{l}
x= \\
y=
\end{array}
\]

Answer

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Answer

\(\boxed{(-4, 7)}\) is the solution to the system of equations

Steps

Step 1 ：Multiply equation (1) by 5 and equation (2) by 3 to get: \(50x + 15y = -95\) and \(27x + 15y = -3\)

Step 2 ：Subtract equation (4) from equation (3) to get: \(23x = -92\)

Step 3 ：Divide by 23 to solve for x: \(x = -92 / 23 = -4\)

Step 4 ：Substitute \(x = -4\) into equation (1) to get: \(-40 + 3y = -19\)

Step 5 ：Solve for y: \(3y = 21\) then \(y = 21 / 3 = 7\)

Step 6 ：\(\boxed{(-4, 7)}\) is the solution to the system of equations