Graph the equations y = -3x + 16 and y = 5x. Write the solution to this system of linear equations by typing the point that they have in common.

Answer 1

Personally, I love Desmos and its graphing calculator! You can find it at desmos.com/calculator.

The quick way to do this is to go there.

Enter the two equations. You'll get two lines, and one point of intersection.

The point is (2,10).

I tried to include my graph, but it won't let me, unfortunately!

If you want the formal math, here it is (it's very similar to your other example).

You have a system of two equations in two variables x and y.

(1) y = -3x + 16 and (2) y = 5x

You can immediately use equation (2) substituted into equation (1).

Hence y = -3x + 16 becomes 5x = -3x + 16

=> 8x = 16

=> x = 2

Now put that value of x in equation (2) to get y =5(2) = 10.

Hence the point is (2,10).

I double-check by putting these values in equation (1).

y = -3x + 16 is 10 = -3(2) + 16 = -6 + 16 = 10 which is correct.

Answer 2

Hopefully you know how to graph a function.

y = -3x + 16

Start at (0,16), go down 3 and right one.

y = 5x

This means b = 0, but mathematicians are lazy and don't write "+ 0." Start at (0,0), go up 5 and right 1.

The point where your lines meet is your solution. Plug in the x and y values to both equations and your point should make both equations true.

(0,16), for example.

16 = -3(0) + 16

I 6 = 16

True

16 = 5(0)

16 = 0

Not true

(0,16) is not where your graphs should meet and is thus not the solution.