Consider the two equations you put a square around, which form a system with no
solution. Solve the equations.
To solve the system of equations, we can start by putting the equations in standard form:
1) x + 2y = 5
2) x + 2y = 7
Comparing the coefficients of x and y in both equations, we can see that they are the same. However, the constant terms on the right side are different (5 and 7). Since the coefficients of x and y match, we can subtract equation 1 from equation 2:
(x + 2y) - (x + 2y) = 7 - 5
0 = 2
This equation, 0 = 2, is not true. It implies that there is no solution that will satisfy both equations simultaneously.
Thus, the system of equations has no solution.
To solve a system of equations, let's consider the two equations:
Equation 1:
x + y = 5
Equation 2:
x + y = 7
We can see that both equations have the same variables and coefficients. By comparing the two equations, we notice that the right-hand sides (constant terms) are different. In this case, the system of equations has no solution because the lines represented by the equations are parallel and will never intersect.
Graphically, if we were to plot these two lines on a graph, they would be perfectly parallel and never cross paths. Thus, there is no combination of values for x and y that can satisfy both equations simultaneously.
To solve a system of linear equations, we can use various methods such as substitution, elimination, or matrix operations. However, if you say that the given system has no solution, it means that the equations are contradictory and cannot be satisfied simultaneously. Let's consider the two equations contained within the square brackets:
Equation 1: [ ]
Equation 2: [ ]
If there is no solution, it implies that the equations are somehow conflicting. To determine that, we need the actual equations themselves. Please provide the equations so that we can continue and explain why there is no solution.