solve it---**Question Number:** 6 **Chart Description:** * Type: Cartesian coordinate plane with a grid. * Axes: X-axis labeled 'x', Y-axis labeled 'y'. Origin labeled 'O' at (0,0). * Scale: Integer units are marked on both axes. X-axis ranges from -1 to 9. Y-axis ranges from -2 to 5. * Elements: Two straight lines are drawn on the grid. * Line 1: A line with negative slope passing through grid points, including (4, 1). * Line 2: A line with positive slope passing through grid points, including (4, 1). * Intersection: The two lines intersect at the point (4, 1). **Question Stem:** The graph of a system of linear equations is shown. The solution to the system is (x, y). What is the value of x ?

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A system of linear equations consists of two or more linear equations with the same variables. The solution to the system is the point where all equations are satisfied simultaneously. Graphically, this is the point where the lines intersect. In this problem, we can see that the two lines intersect at the point (4, 1). Therefore, the solution to the system is x equals 4 and y equals 1. Since the question asks for the value of x, our answer is 4. Let's solve this system algebraically. First, we identify the equations from the graph. The blue line has equation y equals negative x plus 5, and the red line has equation y equals zero point five x minus 1. To find the intersection point, we set these equations equal to each other. Negative x plus 5 equals zero point five x minus 1. Moving all terms with x to the left side, we get negative x minus zero point five x equals negative 1 minus 5. Simplifying, negative 1 point 5 x equals negative 6. Dividing both sides by negative 1 point 5, we get x equals 4. To find y, we substitute x equals 4 into either equation. Using the first equation, y equals negative 4 plus 5, which gives us y equals 1. Therefore, the solution is the point (4, 1), and the value of x is 4. Let's verify our solution by substituting the point (4, 1) back into both original equations. For the first equation, y equals negative x plus 5, we substitute x equals 4. This gives us 1 equals negative 4 plus 5, which simplifies to 1 equals 1. This is true, so our solution satisfies the first equation. For the second equation, y equals zero point five x minus 1, we substitute x equals 4. This gives us 1 equals zero point five times 4 minus 1, which simplifies to 1 equals 2 minus 1, which equals 1. This is also true, so our solution satisfies both equations. Therefore, the point (4, 1) is indeed the solution to the system of linear equations. Since the question asks for the value of x, our answer is 4. Let's summarize what we've learned. A system of linear equations can be solved graphically by finding the intersection point of the lines. It can also be solved algebraically by setting the equations equal and solving for the variables. We've verified that the solution (4, 1) satisfies both original equations. When we substitute x equals 4 and y equals 1 into the first equation, y equals negative x plus 5, we get 1 equals 1, which is true. Similarly, when we substitute into the second equation, y equals zero point five x minus 1, we also get 1 equals 1, which is true. Therefore, the solution to the system is the point (4, 1). Since the question asks for the value of x in the solution, our answer is 4.