Question

Review the graph of a system of two linear equations in two variables : 4x + 3y = 15 and y = x + 5. Find the solution to both equations

Answer 1

[AI-generated answer — Bot GPT 3.5]

To graph the system of linear equations,

4x + 3y = 15
y = x + 5

we can rewrite the second equation as:
y - x = 5

Now, graphing these equations:

Equation 1:
4x + 3y = 15
3y = -4x + 15
y = (-4/3)x + 5

Equation 2:
y = x + 5

Now, plotting the graphs of these two equations:

The first equation is a line with y-intercept 5 and a slope of -4/3, meaning it goes down 4 units for every 3 units it moves to the right.

The second equation is a line with y-intercept 5 and a slope of 1, meaning it goes up 1 unit for every unit it moves to the right.

The solution to this system of equations is the point where the two lines intersect on the graph. Solving for the point of intersection, we get:
y = x + 5
(-4/3)x + 5 = x + 5
-4x + 15 = 3x + 15
-4x - 3x = 0
-7x = 0
x = 0

Plugging in x = 0 into either equation, we get:
y = 0 + 5
y = 5

Therefore, the solution to the system of equations is x = 0, y = 5. This point represents the intersection of the two lines on the graph.