Question

Graph the system of equations

x + y = 7

2x - 4y = 8

My graphing calculator doesn't make any sense, how do I solve this without it?

Answer 1

Solve both of those equations for y.
Objective: Put into y=mx+b form.

Answer 2

y = -x + 7

y = -.5x - 2

Answer 3

I'm not sure about your second equation. I think you should have a positive slope.

Answer 4

y=-x+7
y=x/2-2

Now graph using the y-intercepts and the slopes of each equation.
y=mx+b
(0,b) is the y-intercept
m is the slope

Answer 5

what exactly am i even supposed to be finding though? the x and y intercepts of each line?

Answer 6

Well you said you wanted to solve the system of equations, right?
So you are looking for when the lines meet.
At what point, do they meet?

Answer 7

(6, 1)

Answer 8

Yep. That works. You can always check yourself by pluggin' in your result into both equations to see if both equations hold.
Like so:
(x=6,y=1)

y=-x+7
1=-6+7
1=1 (1=1 is a true statement so (6,1) works for this equation but what about the other)

y=x/2-2
1=6/2-2
1=3-2
1=1 (again this is a true statement)

Since both of our equations hold, that means we have found the correct solution.

Answer 9

i have another one that i'm trying to figure out too.


this one says to solve it algebraically (with substitution or elimination)

5x + y = 9
6x + 10y = 2

Answer 10

if i do it with substitution i get this

5x + y = 9 solved for y is y = -5x + 9

6x + 10(-5x + 9) = 2
6x - 50x + 9 = 2
6x - 50x = -7
-44x = -7
x = .159

which doesnt seem right at all, but if i try it with elimination then i get this

5x + y = 9
6x + 10y = 2

-10(5x + y = 9) = -50x - 10y = -90

-50x - 10y = -90
+ 6x + 10y = 2
----------------------
-44x = -88

x = 2

which seems right


so, if x = 2, then the equations now look like this
10 + y = 9, and
12 + 10y = 2

y = -1 and
10y = -10, or y = -1

Answer 11

well 10(9)=90