Question - Solving System of Linear Equations by Graphing with Same Slope
Solution:
To solve a system of linear equations by graphing, we need to plot each equation on a graph and identify where they intersect.The equations given are:1) x + y = 22) x + y = 3For each equation, we can solve for y to put the equation into slope-intercept form (y = mx + b).For the first equation:x + y = 2y = -x + 2 (subtracting x from both sides)For the second equation:x + y = 3y = -x + 3 (subtracting x from both sides)Now let's graph each equation. We'll start by plotting the y-intercept for each line, which is the point where x = 0.For the first equation (y = -x + 2), when x = 0, y = 2, so we have the point (0, 2).For the second equation (y = -x + 3), when x = 0, y = 3, so we have the point (0, 3).Next, we use the slope, which is -1 (since the coefficient of x is -1 in both equations), to find another point for each line. From our y-intercept (0, 2) for the first equation, move down 1 unit and to the right 1 unit to reach the point (1, 1). Similarly, from the y-intercept (0, 3) for the second equation, move down 1 unit and to the right 1 unit to reach the point (1, 2).Now, we can draw the lines through these points:For the first line: Draw a line through (0, 2) and (1, 1)For the second line: Draw a line through (0, 3) and (1, 2)However, upon examining these two equations, we realize they are parallel and have the same slope but different y-intercepts. Since they are parallel, they will never intersect. This means there is no solution to this system of equations; it is inconsistent.The graph provided in the image seems to be showing the lines incorrectly as they intersect, but that must be a mistake because, theoretically, the two lines cannot intersect given they have the same slope and different y-intercepts.
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