# * Linear/graphing question - Thanks

• nukeman
This is another way to solve the equations simultaneously, using substitution. In summary, the two equations given are L: y = 2x - 5 and M: y = -x + 4. To find the point of intersection of these two lines on a graph, one can either graph the lines and see where they intersect, or solve the equations algebraically using methods such as elimination or substitution.
nukeman

## Homework Statement

L: 2x - y = 5
M: x + y = 4

So I got:

L: y = 2x - 5
M: y = -x + 4

L has a slope of 2 and M has a slope of -1

## Homework Equations

****Now it says find the point of intersection on the graph. How do I plug those points on a graph? Any help would be GREAT!

nukeman said:

## Homework Statement

L: 2x - y = 5
M: x + y = 4

So I got:

L: y = 2x - 5
M: y = -x + 4

L has a slope of 2 and M has a slope of -1

## Homework Equations

****Now it says find the point of intersection on the graph. How do I plug those points on a graph? Any help would be GREAT!

## The Attempt at a Solution

Good job. Now you have two equations and two unknowns (the x and y values that would be where the two lines meet). Have you studied how to solve systems of equations?

Hint -- subtract the 2nd equation from the first one...

berkeman said:
Good job. Now you have two equations and two unknowns (the x and y values that would be where the two lines meet). Have you studied how to solve systems of equations?

Hint -- subtract the 2nd equation from the first one...

Um, no we have not. Thats basically all it says in this certain practice question in our textbook.

Can u help me out on what to do next?

Thanks, appreciate the help :)

nukeman said:
Um, no we have not. Thats basically all it says in this certain practice question in our textbook.

Can u help me out on what to do next?

Thanks, appreciate the help :)

Well, I gave you a hint already on how to solve those two equations simultaneously. You want to manipulate the equations so that you can eliminate one of the two variables, and that let's you get a number for the other one. So you listed your two equations:

L: y = 2x - 5
M: y = -x + 4

Now just subtract the lower equation from the upper one. Like this:
Code:
  (y = 2x - 5)
- (y = -x + 4)
--------------

Negate each term in the 2nd line (distribute the "-" sign through), and add the two lines. The +y and -y cancel to give you 0 on the left of the resulting equation, and you will end up with some x term and some constant term on the right. That let's you solve for x, and then you plug that value of x back into either of your first equations to find the value of y. You can check your x,y answer in both equations L and M to be sure that both equations are satisfied by that x,y point on the graphs. That is where the two lines cross, with a common x,y point.

nukeman said:
Um, no we have not. Thats basically all it says in this certain practice question in our textbook.

Can u help me out on what to do next?

Thanks, appreciate the help :)

How about graphing? Have you learned how to graph an equation of a line in slope-intercept form (y = mx + b)? If so, carefully graph the two lines on graph paper and see where they intersect.

Or, if you have to solve the equations algebraically, the method shown above is solving by elimination. There's also a method known as solving by substitution. Start by setting one of the equations for one of the variables (already done in your case. Then substitute the equation you first manipulated into the other one for that variable. In your case, this means setting the two right sides equal:
2x - 5 = -x + 4
and solve for x. Then substitute the value for x in either of the original equation to solve for y.

## 1. What is a linear/graphing question?

A linear/graphing question is a type of mathematical problem that involves creating a graph to represent a relationship between two variables. The goal is to use the graph to find a solution to the problem.

## 2. How do I solve a linear/graphing question?

To solve a linear/graphing question, you will need to first identify the variables and their relationship. Then, you can plot the points on a graph and use the slope and y-intercept to create a linear equation. Finally, you can use the equation to find the solution to the problem.

## 3. What is the difference between a linear and non-linear graph?

A linear graph has a straight line, while a non-linear graph has a curved or jagged line. In a linear graph, the relationship between the variables is constant, whereas in a non-linear graph, the relationship is changing.

## 4. What is slope and how is it calculated?

Slope is a measure of the steepness of a line on a graph. It is calculated by taking the change in the y-coordinates divided by the change in the x-coordinates. This can be remembered as "rise over run," or (y2 - y1)/(x2 - x1).

## 5. How can I use graphs to solve real-world problems?

Graphs can be used to solve real-world problems by representing data and relationships between variables visually. This allows for easier analysis and identification of patterns, making it easier to find solutions to problems. Additionally, graphs can be used to make predictions and decisions based on the data shown.

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