SOLUTION: Please help me solve this question Equations 4a + 3b = 27 and 5a - 2b = 28 I solved a to = 6 and b = 1 Graph both equations on the same set of axes. Include the vertical

Question 335156: Please help me solve this question
Equations 4a + 3b = 27 and 5a - 2b = 28
I solved a to = 6 and b = 1
Graph both equations on the same set of axes. Include the vertical and horizontal intercepts for each straight line.
I hope someone can help me. Thanks

Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You have correctly solved for the ordered pair that is the solution set to your system of equations. Now for the graphing:

Start with either one of your equations.

Step 1. Pick a value for a. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier.

Step 2. Substitute that value in place of a in your equation. Do the arithmetic and determine the value of b that results.

Step 3. Take the value of a that you selected for step 1 and the value of b that you calculated in step 2 and form an ordered pair (a,b).

Step 4. Plot the ordered pair from Step 3 on your graph. Since we chose to make the ordered pair in alphabetical order, the a value is the distance right or left along the horizontal axis and the b value is the distance up or down along the vertical axis.

Step 5. Repeat steps 1 through 4 with a different value for a.

Step 6. Draw a line across your graph that passes through the two points that you plotted.

Step 7. Repeat steps 1 through 6 using the other equation.

The point where the lines intersect is the solution, because the coordinates of that point will satisfy (read: make true) both of your equations. You need to determine, by inspection of the graph, what the coordinates of that point are and report your answer as an ordered pair, (a,b), using those coordinates. To check your answer, you should substitute this set of coordinates into each of your original equations and verify that you have a true statement for each of the equations.

The point where a line crosses the horizontal axis is the a intercept, and the ordered pair is of the form (,0). The b intercept, (0,), is where the line crosses the vertical axis.

John

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
well, you did ok by solving the both equations simultaneously.

that should have been the hardest part of the battle.

all that's left is to graph both equations on the same set of axes.

if you let x = a, and y = b, then you will be able to graph these equations on a graph with x as the horizontal axis and y as the vertical axis.

rewrite the equations and solve for y in both equations.

4a + 3b = 27 becomes:

4x + 3y = 27 becomes:

3y = -4x + 27 becomes:

y = (-4/3)*x + (27/3) becomes:

y = (-4/3)*x + 9

That's your first equation in slope intercept form.

5a - 2b = 28 becomes:

5x - 2y = 28 becomes:

-2y = -5x + 28 becomes:

2y = 5x - 28 becomes:

y = (5/2)*x - 28/2 becomes:

y = (5/2)*x - 14

That's your second equation in slope intercept form.

All you need to do now is plot some values of x and solve for y in both equations.

Your graph will look like the following:

Graph of equations:

y = (-4/3)*x + 9
and:

y = (5/2)*x - 14

You can see from this graph that the intersection of the 2 lines is at x = 6 and y = 1.

This is the solution to your set of simultaneous equations.

That point is common to the 2 equations and is therefore the intersection of the lines created by the graph of those 2 equations.

x is your horizontal axis and y is your vertical axis.

since x = a and y = b, you could also say that a is your horizontal axis and b is your vertical axis, if you kept the equations with the variables of a and b, rather than the variables of x and y.

instead of getting y = a function of x, you would have gotten b is a function of a.

you would have plotted the value of b for each value of a, rather than plotting the value of y for each value of x.

since the standard is to have x as the horizontal axis and y as the vertical axis, we simply changed your equations by substituting x for a and y for b to make the equations conform to the standards of the graph.

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