Question

What are the solutions to the system of equations y = 5x + 3 and y = 4x + 6?

Answer 1

The solutions to the system of equations y = 5x + 3 and y = 4x + 6 are found by setting the equations equal to each other to get x = 3, and then substituting into one of the equations to find y = 18. So, the solution is the point (3, 18).

Step-by-step explanation:

The student is asking for the solutions to the system of equations y = 5x + 3 and y = 4x + 6. To find the solutions, we need to find the value(s) of x and y that satisfy both equations simultaneously. Since both equations are set equal to y, we can set them equal to each other to find the x-coordinate of the intersection point.

Here is the step-by-step process to find the solution:

1. Set the two equations equal to each other: 5x + 3 = 4x + 6.
2. Subtract 4x from both sides of the equation: x + 3 = 6.
3. Subtract 3 from both sides of the equation: x = 3.
4. Substitute x back into one of the original equations to find y: y = 5(3) + 3 = 15 + 3 = 18.
5. Thus, the solution to the system of equations is (3, 18).

This single point is where the two lines represented by the equations intersect on the graph.

Answer 2

x = 3 , y = 18

Step-by-step explanation:

given the system of equations

y = 5x + 3 → (1)

y = 4x + 6 → (2)

substitute y = 5x + 3 into (2)

5x + 3 = 4x + 6 ( subtract 4x from both sides )

x + 3 = 6 ( subtract 3 from both sides )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

y = 5(3) + 3 = 15 + 3 = 18

the solution is x = 3 , y = 18