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Y=2x-10 Y=4x-8 Using Substitution what is it

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2 Answers

Substitution method of solving a system of equations requires the replacing of an equivalent value of a variable from one equation for the variable in the other.

y = 2x - 10                       Given

4x - 8 = 2x - 10                Substituted the value of y from the 2nd equation for the y of the 1st equation

4x - 8 - 2x = 2x - 10 - 2x   Subtract 2x from each side

2x - 8 = -10                      Simplify

2x - 8 + 8 = -10 + 8           Add 8 to each side

2x = -2                              Simplify

2x/2 = -2/2                        Divide each side by 2

x = -1                                Simplify

Now we need to find y by substituting -1 for x in either equation

y = 2x - 10                         Given

y = 2(-1) - 10                     Substitution

y = -2 - 10                          Simplify

y = -12                               Simplify

The solution is (-1, -12)

 

Comments

Oops.  Typo in one line:

2x/x = -2/2 Divide each side by 2
2x/2 = -2/2 Divide each side by 2

Good answer, John.

First of all, Alicia, let's look at the problem this way, from a geometric perspective:

Draw two lines on the xy-plane, y = 4x - 8 and y = 2x - 10. Conceptually, the answer to the question is the point on the plane where the two lines intersect. One way of solving the problem is to draw the lines on graph paper and figuring out that point; now, we're not allowed to do that, so you can only use this method to check whatever answer you do get.

You are asked to solve the problem by substitution, which means that you need to express y in terms of x or x in terms of y. The first equation tells us that y = 4x - 8 and the second tells us that y = 2x - 10, so we can set up the equation like this:

y = y;

4x - 8 = 2x - 10.

Now we can solve. First subtract by 2x on both sides to get only a number on the right side of the equation:

2x - 8 = -10;

Then add 8 on both sides to get only x's on the left side:

2x = -2;

Finally, divide by 2 to solve for x. You should get x = -1.

We know that y = 4x - 8. Now that we know x = -1, we substitute -1 in for x in the equation:

y = 4 (-1) - 8 = -4 - 8 = -12.

The answer is (-1,-12). Try checking your answer by drawing the two lines like I suggested earlier. You should get that as the intersection point.

Is there anything else that you would like to ask?