1.) Solve the system by graphing. You may use paper or a calculator.
2x - y = 8
x + 3y = 11
2.) The revenue for a certain brand of toothpaste is y = 2.5x where 'x' is the number of tubes of toothpaste sold and 'y' is the total income for selling 'x' tubes. The cost equation is y = 0.9x + 3000, where 'x' is the number of tubes manufactured and 'y' is the cost of producing 'x' tubes. Find the value of 'x' where the company breaks even.
x=?
Please help, thank you!
1.)
Plot a Cartesian coordinate system
1 equation :
For x = 0
- y = 8 Multiply both sides by - 1
y = - 8
For y = 0
2 x = 8 Divide both sides by 2
x = 4
Mark points ( 0 , - 8 )
x = 0 , y = -8
and ( 4 , 0 )
x = 4 , y = 0
and draw line
2 equation:
For x = 0
3 y = 11 Divide both sides by 3
y = 11 / 3 = 3.67
For y = 0
x = 11
Mark points ( 0, 3.67 )
x = 0 , y = 3.67
and ( 11 , 0 )
x = 11 , y = 0
and draw line
Intersection of this two lines is solution of system.
x = 5 , y = 2
OR
2 x - y = 8
y = 2 x - 8
x + 3y = 11
y = ( 11 - x ) / 3
in google type :
functions graphs online
When you see list of resulrt click on :
Draw Function Graphs - Plotter - Rechneronline
When page be open in blue rectangle type:
2 x -8
in gray rectangle type:
( 11 - x ) / 3
In options :
Range x-axis from set :
- 3 to 7
Range y-axis from set:
- 15 to 5
and click option draw
2.)
2.5 x = 0.9 x + 3000 Subtract 0.9 to both sides
2.5 x - 0 . 9 = 0.9 x + 3000 - 0.9
1.6 x = 3000 Divide both sides by 1.6
x = 3000 / 1.6 = 1875
0.9(7x+5)=1.6-(x-3)
1.) To solve the system of equations by graphing, you can follow these steps:
Step 1: Choose a coordinate plane, either by drawing one on paper or using a graphing calculator.
Step 2: For each equation, solve for y in terms of x.
Equation 1: 2x - y = 8
Solving for y: y = 2x - 8
Equation 2: x + 3y = 11
Solving for y: y = (11 - x) / 3
Step 3: Plot the two lines on the coordinate plane using the slope-intercept form (y = mx + b). For each line, find two points by choosing different values for x and substituting them into the equation to find the corresponding y-values. Then plot the points and draw a line through them.
Step 4: The point where the two lines intersect is the solution to the system of equations. To find this point, visually determine where the lines intersect on the graph.
Step 5: Read the x-coordinate and y-coordinate of the intersection point to find the solution.
2.) To find the value of x where the company breaks even, we need to find the point where the revenue equation is equal to the cost equation. Set the two equations equal to each other and solve for x.
The revenue equation is given as y = 2.5x, and the cost equation is given as y = 0.9x + 3000.
Setting them equal: 2.5x = 0.9x + 3000
Combine like terms: 2.5x - 0.9x = 3000
Simplify: 1.6x = 3000
Divide both sides by 1.6: x = 3000 / 1.6
Calculate: x ≈ 1875
The value of x where the company breaks even is approximately 1875.