Question

Solve the system using substitution.
X+Y=8
Y=3X

A. (4,12)
B. (2,6)
C. (1/2, 3/2)
D. (-4,-12)

Answer 1

Answer:

Option B that is (2,6) is correct

Explanation:

We have been given with system of equations

$X+Y=8$ and $Y=3X$

Here, we will substitute the value of $Y=3X$ in $X+Y=8$

We will get $X+3X=8$

Further simplification we will get to $4X=8$

Hence, the value of $X=2$

And now, substituting the value $X=2$ in $Y=3X$ we will get $Y=6$.

Therefore, option B is correct.

Answer 2

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

Further explanation:

It is given that the system of linear equations are $x + y = 8$ and $y = 3x$.

Consider the given equations as follows:

$x + y = 8\,\,\,$      ......(1)

$y = 3x\,\,\,$          ......(2)

From equation (2), the value of $y$ in terms of $x$ is$3x$.

Now, substitute $3x$ for $y$ in the equation (1) as follows:

$x + 3x = 8$

The variable is eliminated in the above equation.

Simplify the equation as follows:

$\begin{aligned}x + 3x&=8\\4x&=8\\x&=\frac{8}{4}\\x&=2\\\end{aligned}$

Therefore, the value of $x$ is $2$.

Substitute $2$ for $x$ in the equation (2) and obtain the value of $y$ as shown below.

$\begin{aligned}y&= 3\left( 2\right)\\&=6\\\end{aligned}$

Therefore, the value of $y$ is $6$.

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

Check whether the obtained solution $(2,6)$ satisfies the given equations or not.

Substitute $2$ for $x$ and $6$ for $y$ in the equation (1) and check the equation.

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

The ordered pair $\left({2,6}\right)$ satisfies the equation (1).

Substitute $2$ for $x$ and $6$ for $y$ in the equation (2) and check the equation.

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

The ordered pair $\left({2,6}\right)$ satisfies the equation (2).

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

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Linear equations

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