SOLUTION: y = x - 8 y = -2x + 1

Question 1204629: y = x - 8
y = -2x + 1
Found 3 solutions by MathLover1, mananth, math_tutor2020:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

.....eq.1
.....eq.2
----------------------------
since left sides equal, right sides must be equal too
so, we have

go to eq.1, substitute
.....eq.1

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
y = x - 8
y = -2x + 1
I assume solve the system
Equate both
x - 8 = -2x + 1
add 2x to both sides
x-8+2x= -2x+1+2x
3x-8 = 1
add 8 to both sides
3x-8+8=1+8
3x=9

divide by 3
x =3
Plug x in y = x - 8
y =3-8= -5

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: (x,y) = (3, -5)

Explanation

I'll graph each equation to show how to get that answer.
You can use a graphing tool like Desmos or GeoGebra to quickly get the answer, but I'll show the step-by-step process by hand.

To graph each line, we plot two points.
Each point is of the form (x,y)
We select any x value we want to get its paired y value.

Plug x = 0 into the 1st equation.
y = x-8
y = 0-8
y = -8
The point (0,-8) is on the line y = x-8

Repeat for x = 1
y = x-8
y = 1-8
y = -7
The point (1,-7) is also on the line y = x-8

Plot the two points (0,-8) and (1,-7) to graph the line y = x-8.

Repeat similar steps for the other equation. Two points on the line y = -2x+1 are (0,1) and (1,-1)

Let's plot the two lines together on the same xy grid.

y = x-8 in green
y = -2x+1 in blue
The two lines intersect at (3, -5)

Let's confirm that solution.
Plug the coordinates into the 1st equation
y = x-8
-5 = 3-8
-5 = -5
The 1st equation is confirmed.
Do the same for the 2nd equation
y = -2x+1
-5 = -2(3)+1
-5 = -6+1
-5 = -5
Both equations have been confirmed true.

More practice with graphing a system of linear equations
https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.1204488.html

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