Verified answer

2x + y = 13

y = -2x + 13

5x-2y=1

-2y = -5x + 1

y = 5/2x - 1/2

Graph

y = -2x + 13 & y = 5/2x - 1/2

Find the point where they intersect and that should be the answer.

Algebraically...

2x+y=13 = y = -2x + 13, right? Plug the y = -2x + 13 in to

5x-2y=1

5x - 2(-2x + 13) = 1

5x + 4x - 26 = 1

9x -26 = 1

9x = 27

x = 3

Now, plug the x value (3 in this case) into the y = -2x + 13 equation to get the y value

y = -2*3 + 13,

y = -6 + 13

y = 7

2x+y=13

y = -2x +13

this line passes through the following 2 points

point A : (x =0 y =13) and point B: (x =6 y =1)

join the the 2 points A and B and extend the line on both sides of line AB

5x-2y=1

y = 5x/2 -1/2

this line passes through the following points

point C: (x = 0 y =-1/2) and

point D : (x =1 y =2)

join the points C and D and extend the line on both sides of line CD

Solving geometrically is to look where the 2 lines intersect and find the point (x,y).

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Algebraically:

2x+y=13 call this equation (1)

5x-2y=1 call this equation (2)

if we add 2 times (1) to (2) we get

9x = 27 x =3

2x +y =13 and x =3 , we get

y =13-2x =13 -6 =7

2x+y=13

standard eqn would be y=-2x+13

2 units down and 1 units right from (0,13) which is the y-intercept will be (1, 11). Draw a line passing thru (0,13) and (1,11) and that will be you first graph.

5x-2y=1

standard eqn will be y=(5/2)x-(1/2)

5 units up and 2 units right from (0,-1/2) wc is the y-int will be (2, 9/2 or 4.5). Draw a line passing thru the aforementioned coordinates.

x-intercept (where y=0) of 2x+y=13 is 13/2 or 6.5. if you graph it will more or less pass thru that point.

x-int of 5x-2y=1 is 1/5 or roughly 0.2. if you graph it, it will likely pass thru there as well.

to solve algebraically:

(2x+y=13)2--> 4x+2y=26

5x-2y=1 cancelling 2y we get 9x=27 therefore x is 3

replacing x in 2x+y=13: 6+y=13, y=7. so our point of interception will be at (3,7).

2x+y=13 ....(1) x=0 than y=13, put x=1,y =11, put x=2, y=9. put x=3, y=7 you get four points(0,13) (1,11) (2,9) (3,7) for equation (1)similarily for equation (2) 5x+2y=1 put x=0 u get y=(-1/2) Put x=1 u get y=2 put x=(-1) u get y=(-3) and so on. Draw graphs.the point of intersaction will be the answer. Check both the equations by putting these values of x & y algebrically.

2x+y=13

-2x -2x

y= -2x+13

5x-2y=1

+2y +2y

5x=2y+1

-1 -1

5x-1=2y

/2 /2

2.5x-.5=y

2.5x-.5=y= -2x+13

+2x +.5 +2x+.5

4.5x=13.5

/4.5 /4.5

x=3

to graph plug y=2.5x-.5 and y= -2x+13 into your graphing calculator

take sample data . draw the graph is a graph paper.

note the intersection point.

You can find the same result by solving algebrically also