Question

A pair of equations is shown below:

y = 2x − 1
y = 4x − 5

Part A: In your own words, explain how you can solve the pair of equations . If solving graphically, write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. If solving by substitution, list the steps. If you decide to solve by elimination, specify the number you multiply the first equation to eliminate x? (6 points)

Part B: What is the solution to the pair of equations?

Answer 1

Part A: To solve the pair of equations, you can use various methods such as graphing, substitution, or elimination.

If solving graphically, you would plot both equations on a graph. For the equation y = 2x - 1, the slope is 2 and the y-intercept is -1. For the equation y = 4x - 5, the slope is 4 and the y-intercept is -5. You would then find the point where the two lines intersect, which represents the solution to the pair of equations.

If solving by substitution, you would first solve one of the equations for either x or y. For example, you could solve the first equation y = 2x - 1 for y. Then, you would substitute this expression for y in the second equation y = 4x - 5. You can then solve for x and use that value to find the corresponding y value.

If you decide to solve by elimination, you would multiply the first equation, y = 2x - 1, by 2 to eliminate x. This would give you 2y = 4x - 2. You can then subtract this new equation from the second equation y = 4x - 5 to eliminate x and solve for y.

Part B: The solution to the pair of equations y = 2x - 1 and y = 4x - 5 is x = 2, y = 3. This means that the values of x and y that satisfy both equations are x = 2 and y = 3.