Mathematics, 22.07.2021 06:00 andreaisabela

Solving systems by substitution how would you you find the answer for
-5x + y = -2
-3x+6y=-12 ? having some issues with how to this

Answers: 2

Show answers

Answers

Answer from: dragon2565

9514 1404 393

(x, y) = (0, -2)

Step-by-step explanation:

When solving by substitution, you usually want to find an expression for one of the variables in terms of the other. So, the first thing you look for is an equation that has a coefficient of 1 or -1 on one of the variables. Recognizing that the second equation's terms all have a common factor of 3, you basically have two choices.

Substitute for y

Using equation 1, you can write an expression for y:

y = 5x -2 . . . . . . add 5x to both sides

Then substituting this into the original equation 2, you have ...

-3x +6(5x -2) = -12

27x -12 = -12 . . . . . . . simplify

27x = 0 . . . . . . . . . add 12

x = 0 . . . . . . . . . divide by 27

y = 5(0) -2 = -2 . . . . find y using the expression for substitution

The solution is (x, y) = (0, -2).

Substitute for x

If you decide you'd rather substitute for x, you can solve the second equation easily for x.

-3x +6y = -12

x -2y = 4 . . . . . . divide by -3

x = 2y +4 . . . . . . add 2y

Substituting for x in the first equation gives ...

-5(2y +4) +y = -2 . . . . substitute for x

-9y -20 = -2 . . . . . . . simplify

-9y = 18 . . . . . . . . . add 20

y = -2 . . . . . . . . . . . divide by -9

x = 2(-2) +4 = 0 . . . . find x using the expression for substitution

The solution is (x, y) = (0, -2).

Additional comment

In some cases, there are no variables that have a coefficient of ±1, so you just need to "bite the bullet" and deal with the resulting fractions.

Example:

solve for y: -5x +2y = -2

2y = 5x -2

y = 5/2x -1 . . . . expression used to substitute for y

Of course, you can multiply the equation after substitution by 2 to eliminate fractions, or just work the problem as is. The point of looking for coefficients of ±1 is to avoid having to do arithmetic with fractions. It can help avoid errors to work with integers, but ultimately the method is the same regardless of the form of the numbers.

You don't always have to substitute for the "bare" variable. Sometimes it can save steps to substitute for expressions instead of variables. If our system of equations were ...

-5x +2y = -2-3x +6y = -12

You can substitute into the second equation for (2y). In that case, the second equation becomes ...

-3x +3(2y) = -12

-3x +3(5x-2) = -12 . . . . . . where 2y = 5x -2

Answer from: Quest

answer: 45

Answer from: Quest

y=1/4x-4

step-by-step explanation:

Here’s a graph of a linear function. write the equation that describes that function

Another question on Mathematics

Mathematics, 21.06.2019 19:50

Type the correct answer in each box. spell all words correctly. a sequence of transformations maps ∆abc onto ∆a″b″c″. the type of transformation that maps ∆abc onto ∆a′b′c′ is a . when ∆a′b′c′ is reflected across the line x = -2 to form ∆a″b″c″, vertex of ∆a″b″c″ will have the same coordinates as b′.

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

The table below lists recommended amounts of food to order for 10 party guests. how much of each food item should nathan and amanda order for a graduation party with 55 guests? use the table to answer. item amount fried chicken 16 pieces lasagna 7 pounds deli meats 1.8 pounds sliced cheese 1 and two fifths pounds bakery buns 1 dozen potato salad 2 pounds

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

10x − 5y + 14 = 0 whats the answer pls

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

Tim has obtained a 3/27 balloon mortgage. after the initial period, he decided to refinance the balloon payment with a new 30-year mortgage. how many years will he be paying for his mortgage in total?

Answers: 2

Answer

You know the right answer?

Solving systems by substitution how would you you find the answer for
-5x + y = -2
-3x+...

Questions