3y-6=3x and y+2x=5 solve the system of linear equations by graphing show work

  (x, y) = (1, 3)

Step-by-step explanation:

The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.

___

If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.

  3y -6 = 3x

To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.

  3x -3y = -6

  x/(-6/3) +y/(-6/-3) = 1

  x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.

Plot the intercept points and draw a line through them.

  y +2x = 5

The intercepts for this one are found by dividing by 5:

  x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.

The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.

  y = -2x + 5

The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).

  Solution

When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.