Question

2x − 3y = 20
2x − 2y = 10

Answer 1

To solve the system of equations:

1. \( 2x - 3y = 20 \) (Equation 1)
2. \( 2x - 2y = 10 \) (Equation 2)

We can use the elimination method or the substitution method. Here, I'll use the elimination method.

First, let's eliminate \( x \) by making the coefficients of \( x \) in both equations equal. Notice that both equations have \( 2x \), so we can simply subtract one equation from the other.

Subtract Equation 2 from Equation 1:
\[
(2x - 3y) - (2x - 2y) = 20 - 10
\]
\[
-3y + 2y = 10
\]
\[
-y = 10
\]
\[
y = -10
\]

Now that we have \( y = -10 \), we can substitute this value back into one of the original equations to find \( x \). We can use Equation 2:
\[
2x - 2(-10) = 10
\]
\[
2x + 20 = 10
\]
\[
2x = 10 - 20
\]
\[
2x = -10
\]
\[
x = -5
\]

Finally, the solution to the system of equations is:
\[
x = -5, \quad y = -10
\]

Thus, the solution is \( (x, y) = (-5, -10) \).