Question

1. 4x - y = 3

-8x + 2y = -6
solution:

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(4x - y=3\), we can rewrite it as \(y = 4x-3\). The slope \(m_1 = 4\) and the y - intercept \(b_1=- 3\).
For the second equation \(-8x + 2y=-6\), divide both sides by 2: \(-4x + y=-3\), then rewrite it as \(y=4x - 3\). The slope \(m_2 = 4\) and the y - intercept \(b_2=-3\).

Step2: Analyze the relationship between the two lines

Since both lines have the same slope (\(m_1=m_2 = 4\)) and the same y - intercept (\(b_1 = b_2=-3\)), the two lines are coincident (they are the same line). To graph the line \(y = 4x-3\):

• Start with the y - intercept: plot the point \((0,-3)\) on the y - axis.
• Use the slope: the slope is \(4=\frac{4}{1}\), which means from the point \((0,-3)\), we move 1 unit to the right (in the positive x - direction) and 4 units up (in the positive y - direction) to get the point \((1,1)\). We can also move 1 unit to the left and 4 units down to get the point \((- 1,-7)\). Then draw a straight line through these points (and all other points that satisfy the equation \(y = 4x-3\)).

Answer:

The two equations represent the same line \(y = 4x - 3\). To graph it, plot the y - intercept \((0,-3)\) and use the slope \(4\) to find other points (e.g., \((1,1)\), \((-1,-7)\)) and draw a straight line through them.