Solving the system y x + 3 x + y = 8 by graphing shows that there is no solution to the system is this statement true of Explain
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The statement is true, because when solving the system by graphing, if the resulting graph does not intersect at any point, it means that there is no solution to the system.
The statement is true. When we graph the equation y + x + 3x + y = 8, we can simplify it to 4x + 2y = 8. By rearranging the equation, we get y = -2x + 4.
When we graph this equation, we find that it represents a straight line. Since the coefficient of x is negative (-2), the line has a negative slope. As we move along the x-axis (from left to right), the value of y decreases.
Now, since this is a single linear equation, it represents a straight line. If we were to graph another linear equation, the intersection point of the two lines would represent the solution to the system of equations.
However, in this case, there is only one equation. Therefore, there is no other line to intersect with, and hence there is no solution to the system of equations.
The statement is true. When solving the system y = x + 3, x + y = 8 by graphing, we can plot the two equations on a graph and look for their intersection point.
For the first equation, y = x + 3, we can choose a few values of x and calculate the corresponding values of y. For example, if we let x = 1, then y = 1 + 3 = 4. If we let x = -1, then y = -1 + 3 = 2. We can repeat this process for other values of x to get several (x, y) coordinate pairs that lie on the line represented by the equation y = x + 3. Plotting these points on a graph and connecting them will give us a straight line.
For the second equation, x + y = 8, we can rearrange the equation to solve for y. If we subtract x from both sides, we get y = 8 - x. We can choose values of x and calculate the corresponding values of y. For example, if we let x = 1, then y = 8 - 1 = 7. If we let x = -1, then y = 8 - (-1) = 9. Plotting these (x, y) coordinate pairs on a graph and connecting them will give us another line.
If we graph both these lines, we will see that they are parallel and do not intersect. Therefore, there is no solution to the system y = x + 3, x + y = 8.