Question

Estimate the solution to the system of these linear equations

y=-2x+3
y=5x-4

Answer 1

To find the solution to the system of equations given by:

1. \( y = -2x + 3 \)
2. \( y = 5x - 4 \)

we can set the two equations equal to each other since both are equal to \( y \):

\[
-2x + 3 = 5x - 4
\]

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

1. Add \( 2x \) to both sides:

\[
3 = 7x - 4
\]

2. Add \( 4 \) to both sides:

\[
7 = 7x
\]

3. Divide both sides by \( 7 \):

\[
x = 1
\]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). Using the first equation:

\[
y = -2(1) + 3 = -2 + 3 = 1
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (1, 1)
\]

So, the point of intersection (the solution to the system) is \( (1, 1) \).