#### Question

# Math help please! 10 points!?

Solve this system of equations by graphing. I am aware that you cannot show me the graph....I just need help solving the equations, to get the points to plot on the graph. Thanks in advance! Details would be great :-)

2x - y = -1

5x + 4y = 17

#### Answer

This is simultaneous equations. There are several methods: substiution, elimination and addition. I will show you the Substitution method.

Substitution:

2x - y = -1

2x = -1 + y

2x + 1 = y (*)

Just move the unknowns around until there is an expression y = ax + b or y = ax^2 + b or.......depends on the question. Since both x and y have powers of 1, substitution is a good method to use.

Now, the second equation given is: 5x + 4y = 17. Substitute the y in this equation with the other equation you derived (*).

5x + 4y = 17

5x + 4(2x + 1) = 17

5x + 8x + 4 = 17

13x = 17 - 4

x = 13/13

x = 1

Lastly, substitute x = 1 into the equation (*),

y = 2x + 1

y = 2(1) + 1

y = 3

When you draw the graph, there will be one point of intersection between the two straight lines. That point is x =1, y = 3, or in coordinate form, (1,3). And that's it.

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2x - y = -1

5x + 4y = 17

4(2x - y = - 1)

5x + 4y = 17

8x - 4y = -4

5x + 4y = 17

_________

13x - 0 = 13

x = 13 - 13 = 0

5(0) + 4y = 17

4y = 17

y = 17/4

basically its telling you to graph both lines, wherever they intersect is your answer.

y=mx+b

y=2x+1

1 is your y intercept, 2 is your slope.

y=-5/4x+17/4

17/4 is your y intercept, -5/4 is your slope.

have fun graphing!

ok so you want to have either the x or the y be equal. Let's make the y's be equal. Multiply the 1st equation by 4 ..your new equation should look like this: 8x - 4y = -4

5x +4y = 17

Now you want to cancel out the y's.

You want to add the 2 equations.

8x - 4y = -4

+5x + 4y = 17

_______________

13x = 13

Now you want to solve for x. x should equal 1.

Now all you have to do is plug 1 in for x and solve for y.

You can plug it back into either equation.

5(1) + 4y = 17

-5. -5

4y =12

-- --

3. 3

y = 4

Your points on the graph are (1, 4)

I hope I helped you and that you understand now!

For each equation, it's helpful to get y alone.

2x-y=-1 ~> 2x+1 = y

5x + 4y = 17 ~> (17-5x)/4 = y

Once you get it into that form, start choosing x values. Values such as 0-10 is a good place to start.

What ever you put in for x, you will plot that number as your x value for the point on the graph. The number you get after you put in x will be your y value.

EX:

x=0 ~> 2(0)+1=y ~> 1=y ~> Plot (0,1)

When you're done, the point where both graphs meet will be your answer for your x and y for the system of equations.

This is pretty simple just subtract x from both sides then divide by y's coefficient (the number in front of y). It would look like this for both problems.

2x-y=-1

-y=-2x-1 (subtract 2x from both sides)

y=2x+1 (divide both sides my -1 to change all of the signs because you need to solve for y not -y)

There's your answer for that one now for the other one.

5x+4y=17

4y=-5x+17 (again subtract 5x from both sides)

y=(-5x/4)+(17/4) (divide both sides by 4 to solve for y and get y equals negative 5x divided by 4 plus 17 divided by 4)

I hope that helps enough for your graph!