Question

y=4x-3
y=-2x+9

Answer 1

To find the point of intersection of the two lines given by the equations \( y = 4x - 3 \) and \( y = -2x + 9 \), we can set the right-hand sides of the equations equal to each other since they are both equal to \( y \).

So we set:

\[
4x - 3 = -2x + 9
\]

Now, we can solve for \( x \):

1. Add \( 2x \) to both sides:
\[
4x + 2x - 3 = 9
\]
\[
6x - 3 = 9
\]

2. Add \( 3 \) to both sides:
\[
6x = 12
\]

3. Divide by \( 6 \):
\[
x = 2
\]

Now that we have the value of \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the first equation \( y = 4x - 3 \):

\[
y = 4(2) - 3
\]
\[
y = 8 - 3
\]
\[
y = 5
\]

Thus, the point of intersection of the two lines is:

\[
\boxed{(2, 5)}
\]

You can also verify by substituting \( x = 2 \) into the second equation \( y = -2x + 9 \):

\[
y = -2(2) + 9
\]
\[
y = -4 + 9
\]
\[
y = 5
\]

Hence, the intersection point \( (2, 5) \) is confirmed.