Question

Solve the system of equations by substitution.

6 = −4x + y −5x − y = 21
Answer:


Solve the system by the elimination method.
2x + y = 20 6x – 5y = 12
Answer:

Answer 1

To solve systems of equations, substitution involves expressing one variable in terms of another and substituting, whereas elimination involves aligning equations and eliminating one variable to solve for the other.

Step-by-step explanation:

To solve the system of equations by substitution, you need to isolate one variable in one equation and then substitute that expression into the other equation. For the first system given:

1. From equation 6 = -4x + y, express y as y = 6 + 4x.
2. Substitute y in the second equation -5x - y = 21, which gives us -5x - (6 + 4x) = 21.
3. Simplify and solve for x.
4. Once x is found, substitute back into the expression for y to find the value of y.

To solve the system by the elimination method:

1. Arrange both equations in the standard form (Ax + By = C).
2. Multiply one or both equations by a number that will allow the coefficients of one of the variables to be the same (or additive inverses).
3. Add or subtract the equations to eliminate one variable.
4. Solve for the remaining variable.
5. Substitute that back into one of the original equations to find the other variable.

Answer 2

6 = −4x + y

−5x − y = 21

Answer: (-3, -6)

2x + y = 20 6x – 5y = 12

Answer:

(7 , 6)

Step-by-step explanation:

Solve the system of equations by substitution.

6 = −4x + y --> y = 4x + 6

−5x − y = 21

Substitute y = 4x + 6 into −5x − y = 21

−5x − (4x + 6) = 21

-5x - 4x - 6 = 21

-9x = 27

x = - 3

y = 4(-3) + 6

y = -12 + 6

y = -6

(-3, -6)

Solve the system by the elimination method.

2x + y = 20

multiply the equation by (-3) ; 2x + y = 20 so

-6x - 3y = - 60

6x – 5y = 12

------------------add

-8y = - 48

y = 6

2x + y = 20

2x + 6 = 20

2x = 14

x = 7

(7 , 6)