To find the solution to the system of equations, we can set the two equations equal to each other since they both equal \( y \).
Starting with the given equations:
\[ y = -5x + 6 \]
\[ y = -3x - 4 \]
We set them equal to each other:
\[ -5x + 6 = -3x - 4 \]
To solve for \( x \), we first get all \( x \)-terms on one side and constant terms on the other:
\[ -5x + 3x = -4 - 6 \]
\[ -2x = -10 \]
Next, divide by \(-2\):
\[ x = 5 \]
Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). Let's use the first equation:
\[ y = -5x + 6 \]
\[ y = -5(5) + 6 \]
\[ y = -25 + 6 \]
\[ y = -19 \]
So, the solution to the system of equations is:
\[ (x, y) = (5, -19) \]
Thus, the correct answer is:
\[ (5, -19) \]
11.
What is the solution of the system of equations?
y = –5x + 6
y = –3x – 4
(–1, –1)
(–1.25, 12.25)
(5, –19)
(–19, 5)
1 answer