What is the value of the x variable in the solution to the following system of equations for 4x+ 2y =6 x-y=3

x = -1

Step-by-step explanation:

To start with, we can solve for y in 4x + 2y = 6. We want to find the y so we can insert it into our second equation to find out what our x-variable is.

We are going to want to get y by itself, so we can subtract the positive 4x and move it onto the right side.

4x + 2y = 6

2y + 4x - 4x = 6 - 4x

2y = 6 - 4x

2y = -4x + 6

Now that we have this, we still want to get y by itself. Y has a coefficient in front of it, so we are going to want to get rid of that. Because y is being multiplied by 2, we can do the opposite and divide the entire equation by 2. The 2y would be divided by 2, the -4x would be divided by 2, and the 6 would be divided by 2.

This leaves us with: y = -2x + 3.

Now that we know what our y is equal to, we can insert this into our second equation of x - y = 3.

x - y = 3

Let's replace y with what we now know y is equivalent to: -2x + 3.

x - (-2x) + 3.

Subtracting a negative number is equivalent to addition, so we can turn that into an addition sign now:

x + 2x + 3

3x + 3 = 0

Remembering the question, we want to get the x variable alone because that is what we want to solve for. Let's do that now by moving the 3 onto the right side. Since we are adding it, we can subtract it to move it over. Like this:

3x + 3 = 0

3x + 3 - 3 = 0 - 3

3x = -3

Now, like we did in the beginning of this problem, we want the x alone, and because it is being multiplied by x, we can divide the entire problem by 3. -3 will get divided by 3 which will give us -1.

x = -1

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.

step-by-step explanation: