Solve the system of equations y = 2x + 3 and 4x - 2y = -6 using a graphical method.

-1

Step-by-step explanation:

You are asked to solve this set by substitution. Note that the first equation defines

the value of y in terms of x. Therefore, you can use the right side of this equation

(2x + 3) as a substitution for y in the second equation. When you substitute 2x +3 for y

in the second equation, the result is:

.

2x + 3 = 4x + 7

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Let's set the goal of getting all the terms that contain x isolated on the left side of

the equal sign and all the constants by themselves on the right side. Begin by getting rid

of the +3 on the left side by subtracting 3 from the left side. But if you subtract

3 from the left side you must also subtract 3 from the right side. These subtractions

result in the following sequence:

.

2x + 3 - 3 = 4x + 7 - 3

.

Combining numbers on the left side and on the right side simplifies the equation to:

.

2x = 4x + 4

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Now, in a similar fashion, let's get rid of the 4x on the right side by subtracting

4x from the right side. When we do this subtraction, to keep the equation in balance

we must also subtract 4x from the left side. This results in:

.

2x - 4x = 4x - 4x + 4

.

On both sides of the equation combine terms containing x to get:

.

-2x = 4

.

Finally, solve for x by dividing both sides of the equation by -2 because -2 is the multiplier

of x. This results in:

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x = 4/-2 = -2

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So now that we know x = -2, we can return to either one of the original equations  

in the equation set and substitute -2 for x. Then we can solve for y. Let's return

to the first equation and substitute -2 for x. This begins with:

.

y = 2x + 3

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Then substituting -2 for x gives:

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y = 2*(-2) + 3 = -4 + 3 = -1

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

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:

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