Estimate the solution to the system of these linear equations. Y=5x+10, y=-2x+3. A. (1,5) b. (-1,5) c. (-1,-5) d.(5,-1)

Answer 1

To estimate the solution to the system of linear equations \( y = 5x + 10 \) and \( y = -2x + 3 \), we need to find the point of intersection of these two lines. This can be done by setting the equations equal to each other and solving for \( x \):

\[ 5x + 10 = -2x + 3 \]

First, we'll move all terms involving \( x \) to one side and constant terms to the other side:

\[ 5x + 2x = 3 - 10 \]
\[ 7x = -7 \]

Next, we solve for \( x \):

\[ x = \frac{-7}{7} \]
\[ x = -1 \]

Now, we substitute \( x = -1 \) into one of the original equations to find \( y \). Using \( y = 5x + 10 \):

\[ y = 5(-1) + 10 \]
\[ y = -5 + 10 \]
\[ y = 5 \]

So, the point of intersection is \( (-1, 5) \).

Thus, the correct answer is:
b. \((-1, 5)\)