How do you solve the system of equations 5x + y = 9 and 3x + 2y = 4?

1. Rearranging the first equation:

y = 9 - 5x

2. Now we’ll substitute this expression for y into the second equation:

3x + 2(9 - 5x) = 4

3. Simplifying the equation:

3x + 18 - 10x = 4

4. Combine like terms:

-7x + 18 = 4

5. Move 18 to the other side:

-7x = 4 - 18

-7x = -14

6. Divide by -7:

x = 2

Now that we have x, we can substitute it back into the expression we found for y:

y = 9 - 5(2)

y = 9 - 10

y = -1

So the solution to the system of equations is x = 2 and y = -1. In summary:

• x: 2
• y: -1

This means that the point (2, -1) is the intersection of the two lines represented by the equations in the coordinate plane.