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:
\(\begin{aligned}4x+2(1-2x)&=-2\\4x+2-4x&=-2\\2&
eq -2\end{aligned}\)
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: https://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.
