Solve the system using substitution.

x + y = 8

y = 3x

a. (4, 12)

b. (2, 6)

c. (1/2, 3/2)

d. (-4, -12)

Skip to content# Solve the system using substitution. x + y = 8 y = 3x a. (4, 12) b. (2, 6) c. (1/2, 3/2) d. (-4, -12)

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Solve the system using substitution.

x + y = 8

y = 3x

a. (4, 12)

b. (2, 6)

c. (1/2, 3/2)

d. (-4, -12)

X=2 because add the x value to get 4 and then divide

X+y=8

y=3x

You would want to substitute the y for the 3x

x+3x=8

You can now add the x with the 3x to get 4x

4x=8

Now divide the 4 on both side to solve for x

x=2

Now to solve for y just substitute the x for the 2

y=3(2)

Now multiply the 3 and the 2 to solve for y.

y=6

So your corrct answer is B:(2,6)

b

Step-by-step explanation:

x+3x=8

4x=8

x=8÷4

=2

y=3×2

=6

(x,y)=(2,6)

hopefully it works for you

The solution set for the system of linear equations [tex]x + y = 8[/tex] and [tex]y = 3x[/tex] is [tex]\boxed{\left\{{\left({{\mathbf{2,6}}}\right)}\right\}}[/tex].

Further explanation:

It is given that the system of linear equations are [tex]x + y = 8[/tex] and [tex]y = 3x[/tex].

Consider the given equations as follows:

[tex]x + y = 8\,\,\,[/tex] ......(1)

[tex]y = 3x\,\,\,[/tex] ......(2)

From equation (2), the value of [tex]y[/tex] in terms of [tex]x[/tex] is[tex]3x[/tex].

Now, substitute [tex]3x[/tex] for [tex]y[/tex] in the equation (1) as follows:

[tex]x + 3x = 8[/tex]

The variable is eliminated in the above equation.

Simplify the equation as follows:

[tex]\begin{aligned}x + 3x&=8\\4x&=8\\x&=\frac{8}{4}\\x&=2\\\end{aligned}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]2[/tex].

Substitute [tex]2[/tex] for [tex]x[/tex] in the equation (2) and obtain the value of [tex]y[/tex] as shown below.

[tex]\begin{aligned}y&= 3\left( 2\right)\\&=6\\\end{aligned}[/tex]

Therefore, the value of [tex]y[/tex] is [tex]6[/tex].

Thus, the ordered pair for the given system of linear equation is [tex]\left({{\mathbf{2,6}}} \right)[/tex].

Check whether the obtained solution [tex](2,6)[/tex] satisfies the given equations or not.

Substitute [tex]2[/tex] for [tex]x[/tex] and [tex]6[/tex] for [tex]y[/tex] in the equation (1) and check the equation.

[tex]\begin{aligned}2 + 6\mathop&_=^? 8\hfill \\\,\,\,\,\,\,\,8 &= 8\,\,\,\hfill\\\end{aligned}[/tex] (True)

The ordered pair [tex]\left({2,6}\right)[/tex] satisfies the equation (1).

Substitute [tex]2[/tex] for [tex]x[/tex] and [tex]6[/tex] for [tex]y[/tex] in the equation (2) and check the equation.

[tex]\begin{aligned}6\mathop&_= ^? \:3\left( 2 \right)\hfill\\6&= 6\,\,\,\,\,\,\,\,\,\,\,\,\hfill\\\end{aligned}[/tex] (True)

The ordered pair [tex]\left({2,6}\right)[/tex] satisfies the equation (2).

Thus, the solution set for the system of linear equations [tex]x + y = 8[/tex] and [tex]y = 3x[/tex] is [tex]\boxed{\left\{{\left({{\mathbf{2,6}}}\right)}\right\}}[/tex].

Learn more:

1. Which classification best describes the following system of equations?

2. Which polynomial is

3. Write the subtraction fact two ways 10-3?

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Linear equations

Keywords: Substitution, linear equation, system of linear equations in two variables, variables, mathematics,[tex]x + y = 8[/tex] ,[tex]y = 3x[/tex] , solution set

Okay sub equation 2 into equation 1:

so it becomes

x + 3x = 8

4x = 8

x = 2

then 2 + y = 8, therefore y = 6

So the answer is B

X+3x=8

x=8-3x is how far i could simplify

Option B that is (2,6) is correct

Explanation:

We have been given with system of equations

[tex]X+Y=8[/tex] and [tex]Y=3X[/tex]

Here, we will substitute the value of [tex]Y=3X[/tex] in [tex]X+Y=8[/tex]

We will get [tex]X+3X=8[/tex]

Further simplification we will get to [tex]4X=8[/tex]

Hence, the value of [tex]X=2[/tex]

And now, substituting the value [tex]X=2[/tex] in [tex]Y=3X[/tex] we will get [tex]Y=6[/tex].

Therefore, option B is correct.

X=2 y=6 2+6=8 and 3 times 2 =6