Question

a system of linear equations is shown.
y = -3x + 2
5x + 3y = 0
what is the y-coordinate of the solution to this system?
a -1/7
b -5/2
c -7/4
d 3/2

Answer 1

To find the y-coordinate of the solution to the system of linear equations given by:

1. \( y = -3x + 2 \)
2. \( 5x + 3y = 0 \)

we can substitute the expression for \( y \) from the first equation into the second equation.

Substituting \( y = -3x + 2 \) into \( 5x + 3y = 0 \):

\[
5x + 3(-3x + 2) = 0
\]

Now, simplify the equation:

\[
5x - 9x + 6 = 0
\]

Combine like terms:

\[
-4x + 6 = 0
\]

Now solve for \( x \):

\[
-4x = -6
\]
\[
x = \frac{-6}{-4} = \frac{3}{2}
\]

Now, substitute \( x = \frac{3}{2} \) back into the first equation to find \( y \):

\[
y = -3\left(\frac{3}{2}\right) + 2
\]

Calculating this gives:

\[
y = -\frac{9}{2} + 2
\]
\[
y = -\frac{9}{2} + \frac{4}{2} = -\frac{5}{2}
\]

So, the y-coordinate of the solution to the system is \( \boxed{-\frac{5}{2}} \). Thus, the correct answer is \( b. -\frac{5}{2} \).