Question

Solve the system of equations by substitution. What is the solution for x?. . 2x + y = 1 . 4x + 2y = −2

Answer 1

Answer:

Given the system of equation:

2x+y = 1                   .....[1]

4x+2y = -2                .....[2]

We can write equation [1] as:

y = 1-2x

Substitute the value of y in [2] we have;

$4x+2(1-2x) = -2$

Using distributive property, $a \cdot(b+c) = a\cdot b+ a\cdot c$

then;

$4x+2-4x = -2$

Combine like terms;

$2= -2$      False.

Therefore, there is no solution and x = ∅

Answer 2

The system of equations has $\boxed{\text{\bf no solution}}$.

Further explanation:

Given information:  

The system of equation is as follows:

$\boxed{\begin{aligned}2x+y&=1\\4x+2y&=-2\end{aligned}}$

Calculation:

The given equations are  as follows:

$2x+y=1$                      .....(1)

$4x+2y=-2$                      …… (2)

Simplify equation (1) as  follows:

$\begin{aligned}2x+y&=1\\y&=1-2x\end{aligned}$    

Substitute $1-2x$ in place of $y$ in equation (2) as follows:

$4x+2(1-2x)=-2$

Use distributive property to expand the brackets as follows:

$\begin{aligned}4x+2(1-2x)&=-2\\4x+2-4x&=-2\\2&\neq -2\end{aligned}$

The above result obtained is not possible, then any value of $x$ and $y$ will not satisfy the given equations.

This implies that the system is inconsistent.  

Therefore, there is $\boxed{\text{\bf no solution}}$ to the given system of equations.

Graph:

To graph the line, first make a table of set of values. Then plot the points from the table and join the points to obtain the graph.

Equation (1) is expressed as follows:

$y=1-2x$             …… (3)                                              

Substitute $0$ for $x$ in above equation to obtain the corresponding value of $y$ as,

$\begin{aligned}y&=1-(2\times 0)\\y&=1\end{aligned}$  

Substitute $3$ for $x$ in equation (3) to obtain the corresponding value of $y$ as,

$\begin{aligned}y&=1-(3\times 3)\\&=1-9\\&=-8\end{aligned}$  

Now, make the table with the set of values as shown in Table 1.  

Equation (2) is expressed as follows:

$\begin{aligned}2y&=-2-4x\\2y&=2(-1-2x)\\y&=-1-2x\end{aligned}$   Substitute $0$ for $x$ in equation (4) to obtain the corresponding value of $y$ as,

$y=-1$  

Substitute $2$ for $x$ in equation (4) to obtain the corresponding value of $y$ as,

$\begin{aligned}y&=-1-(2\times 2)\\&=-1-4\\&=-5\end{aligned}$  

Now, make the table with the set of values as shown in Table 2.

Now, plot the points and join them with a straight line to obtain the graph of the lines.

The graph of the lines is shown in Figure 1.

In Figure 1, the equation of blue line is $4x+2y=-2$ and the equation of red line is $2x+y=1$.

And also it is seen that both the lines are parallel to each other.

Therefore, the system of equations has $\boxed{\text{\bf no solution}}$.

Learn more:

1. A problem on graph https: //brainly.com/question/2491745

2. A problem on linear equation: brainly.com/question/1473992

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations

Keywords: Solve, system, equations, substitution, solution, 2x+y=1, 4x+2y=-2, graph, linear, parallel, no solution, inconsistent, distributive property, linear equation.