Question

help

Answer 1

What is the value of the y variable in the solution to the following system of equations?
3x - 6y = 12
-2x + 3y = 6

-14

24

14

-24

Answer 2

use the sub. method

Answer 3

or the elim. method

Answer 4

first example:
Elimination method:
Solve the system of equations 2 times x plus 3 times y equals 2 and 9 times x minus 3 times y equals 42 using the elimination method.

Take a look at the 2 times x and 9 times x. 2 times x and 9 times x. If you were to add these terms together, would they cancel out? Nope! If you added 2 times x and 9 times x together, you would get 11 times x.

Now, look at plus 3 times y and minus 3 times y. 3 times y and minus 3 times y. What would happen if you added these terms together? They would add to 0 or cancel out! This problem is already set up to use the Elimination Method easily!

First, add the two equations together. Do this by adding like terms from both equations. Notice that the y-variable canceled out! Don’t forget to add all parts of both equations. The result is the simple equation 11 times x equals 44.

Now, divide both sides by 11 to solve for x. x equals 4.

Remember, when you are solving a system, you need to find both an x- and y-value. Substitute 4 in for x in either of the original equations. 4 is substituted back into the equation 2 times x plus 3 times y equals 2. The equation becomes 2 times 4 plus 3 times y equals 2. 2 times 4 becomes 8. 8 is subtracted from both sides of the equation, which simplifies to be 3 times y equals negative six. Then, 3 is divided from both sides of the equation. y equals negative 2.

The solution to this system is 4 comma negative 2. Recall, this means that 4 comma negative 2 is the point of intersection for the two lines, and the pair of values that will make both equations true.

Answer 5

first example:
Substituion method:
Solve the following system of equations using the substitution method. 2 times x plus y equals 11. 4 times x minus 3 times y equals 7.

The first step is to determine which variable you want to isolate. Look at the 2 equations. There are 4 options. The x and y in both the given equations are highlighted. We could isolate x or y in the first or second equation. However, one of the options, in this case, would make the rest of the steps easier to deal with.

Solving for y in the first equation would require less work in the remaining steps. This is because y, in the first equation, has a coefficient of 1, which means you will not need to divide both sides of the equation by anything to isolate the y. This possibly eliminates having to deal with fractions later on.

So, to isolate y in the first equation, you just subtract 2 x from both sides. The simplified equation is y equal 11 minus 2 times x.

Step 2 is to substitute the expression for the isolated variable into the other equation and solve for the other variable.

Since you know y is equal to (the same as) 11 minus 2 times x in the first equation, you can substitute that expression for y in the second equation. Now, you have an equation with one variable. 4 x minus 3 times the quantity 11 minus 2 times x equals 7.

This equation can then be simplified and solved for x. First, distribute the negative 3 to both the 11 and the negative 2 times x. The equation is now 4 times x minus 33 plus 6 times x equals 7.

Now, combine like terms on the left-hand side, and isolate x. The equation simplifies to 10 times x minus 33 equals 7 when like terms are combined.

Add 33 to both sides.

Then, divide both sides by 10. x equals 4.

The final step is to substitute the value of the first variable into one of the original equations and solve for the second variable.

Here, you will substitute 4 for x into either of the original equations and solve for y. The steps for using the first equation are shown here, but using the second equation will give the same value for y too. 4 is substituted into the equation 4 times x minus 3 y equals 7 to give the equation 4 times 4 minus 3 times y equals 7. The equation is simplified by multiplying 4 times 4. Next, 16 is subtracted from both sides of the equation, and then negative 3 is divided from both sides. y equals 3.

The solution is x equals 4, y equals 3. This means the 2 lines intersect at the point 4 comma 3.

Check your answer! The values 4, 3, should make both equations true (if it’s the correct solution). In order to check you answer, substitute the values 4 for x and 3 for y in both equations. The values are substituted into the first equation and after simplifying the result is 11 equals 11, which is a true statement. The values are also substituted into the second equation which when simplifying results in the true statement 7 equals 7.

Answer 6

that diddnt answer my question but thanks lol