Question

A pair of equations is shown below:

y = 6x − 4
y = 5x − 3

Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)

Part B: What is the solution to the pair of equations? (4 points)

Answer 1

So, both equations are essentially linear equations.
Linear equations are written in the format y = mx+b, where m represents the slope/slope intercept and b represents the y-intercept.
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Part A
the slope and y-intercept

y = mx +b
m - the slope; b- y-intercept

therefore;

y = 6x - 4
m = 6; b = -4

y = 5x - 3
m = 5; b = -3

The coordinates of the point where the lines are crossed are the solution to the system of linear equations.

How to graph the lines:
y = 6x - 4
y-intercept (0; -4)
for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)

y = 5x - 3
y-intercept (0; -3)
for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)

***look at the img for graph reference***

Part B: x = 1; y = 2