Question

Y=6x+10
Y=4x
Solve by substitution

Answer 1

To solve the system of equations by substitution, follow these steps:

1. **Set the equations:**
\[
Y = 6x + 10 \quad (1)
\]
\[
Y = 4x \quad (2)
\]

2. **Substitute equation (2) into equation (1):**
Since both equations equal \(Y\), we can set them equal to each other:
\[
6x + 10 = 4x
\]

3. **Solve for \(x\):**
Subtract \(4x\) from both sides:
\[
6x - 4x + 10 = 0
\]
This simplifies to:
\[
2x + 10 = 0
\]
Now, subtract 10 from both sides:
\[
2x = -10
\]
Divide by 2:
\[
x = -5
\]

4. **Substitute \(x\) back into either equation to find \(Y\):**
We can use equation (2):
\[
Y = 4x = 4(-5) = -20
\]
So, \(Y = -20\).

5. **Write the solution as an ordered pair:**
The solution to the system of equations is:
\[
(x, Y) = (-5, -20)
\]

Thus, the solution to the system of equations is \((-5, -20)\).