Question

Y=3x-50
Y=-2x
Solve by substitution

Answer 1

To solve the system of equations using substitution, we'll follow these steps:

1. We have the two equations:
\[
Y = 3x - 50 \quad \text{(1)}
\]
\[
Y = -2x \quad \text{(2)}
\]

2. Since both equations equal \(Y\), we can set them equal to each other:
\[
3x - 50 = -2x
\]

3. Now, let's solve for \(x\):
- First, add \(2x\) to both sides:
\[
3x + 2x - 50 = 0
\]
\[
5x - 50 = 0
\]

- Next, add 50 to both sides:
\[
5x = 50
\]

- Finally, divide by 5:
\[
x = 10
\]

4. Now that we have \(x\), we can substitute this value back into either of the original equations to find \(Y\). We'll use equation (2):
\[
Y = -2x
\]
Substituting \(x = 10\):
\[
Y = -2(10) = -20
\]

5. So, the solution to the system of equations is:
\[
(x, Y) = (10, -20)
\]

Thus, the result is \(x = 10\) and \(Y = -20\).