Question

Y=1/2x+5;2y=2x+4 Solve by using the substitution method.

Answer 1

Answer:x

=

6

and

y

=

−

8

through systems of equations.

Explanation:

This is known as a system of equations. For this system, we are going to use substitution, since you already know what y is equal to.

As you can see,

y

=

−

1

2

x

−

5

. Since we have

y

directly set equal to something, we can substitute it in for

y

anywhere we want. In this case we will substitute it in for

y

in your first equation.

x

−

2

y

=

2

⇒

x

−

2

(

−

1

2

x

−

5

)

=

2

Through algebraic equation steps, we can simplify the equation to be

x

+

x

−

10

=

2

, and solve the equation for

x

=

6

.

Now that we have the

x

value, we can substitute it in to the

y

equation.

y

=

−

1

2

(

6

)

−

5

When simplified, you get

y

=

−

3

−

5

, or

y

=

−

8

. And remember, if you'd like to check your answer, simply plug your numbers back in for the variables.

y

=

−

1

2

x

−

5

⇒

(

−

8

)

=

−

1

2

(

6

)

−

5

, and when simplified,

−

8

=

−

8

.x

=

6

and

y

=

−

8

through systems of equations.

Explanation:

This is known as a system of equations. For this system, we are going to use substitution, since you already know what y is equal to.

As you can see,

y

=

−

1

2

x

−

5

. Since we have

y

directly set equal to something, we can substitute it in for

y

anywhere we want. In this case we will substitute it in for

y

in your first equation.

x

−

2

y

=

2

⇒

x

−

2

(

−

1

2

x

−

5

)

=

2

Through algebraic equation steps, we can simplify the equation to be

x

+

x

−

10

=

2

, and solve the equation for

x

=

6

.

Now that we have the

x

value, we can substitute it in to the

y

equation.

y

=

−

1

2

(

6

)

−

5

When simplified, you get

y

=

−

3

−

5

, or

y

=

−

8

. And remember, if you'd like to check your answer, simply plug your numbers back in for the variables.

y

=

−

1

2

x

−

5

⇒

(

−

8

)

=

−

1

2

(

6

)

−

5

, and when simplified,

−

8

=

−

8

.

Step-by-step explanation: