Question

Review the graphs of a system of these two linear equations in two variables: y=4x-10 and y=-2x+8 find the solution of the system. The solution of the system of equations is ( )

Answer 1

To find the solution of the system of equations y=4x-10 and y=-2x+8, we need to find the point of intersection between the two lines represented by these equations.

The first equation y=4x-10 is a line with a slope of 4 and a y-intercept of -10. This means that the line goes up 4 units for every 1 unit it goes to the right. It intersects the y-axis at point (0, -10).

The second equation y=-2x+8 is a line with a slope of -2 and a y-intercept of 8. This means that the line goes down 2 units for every 1 unit it goes to the right. It intersects the y-axis at point (0, 8).

To find the point of intersection, we can set the two equations equal to each other:

4x - 10 = -2x + 8

To simplify, let's add 2x to both sides:

6x - 10 = 8

Then, let's add 10 to both sides:

6x = 18

Finally, divide both sides by 6:

x = 3

Plugging this value back into either of the original equations, we can find the y-coordinate:

y = 4(3) - 10 = 12 - 10 = 2

Therefore, the solution to the system of equations y=4x-10 and y=-2x+8 is (3, 2).