Review the graphs of a system of two linear equations in two variables: 4x+3y=15 and y=x+5. Find the solution to both equations.
To find the solution to both equations, we first need to solve the system of equations by graphing them.
1. Graph of 4x + 3y = 15:
To graph this equation, we first need to find the x and y intercepts.
When x = 0, 4(0) + 3y = 15
3y = 15
y = 5
So, the y-intercept is at (0, 5).
When y = 0, 4x + 3(0) = 15
4x = 15
x = 3.75
So, the x-intercept is at (3.75, 0).
Now, draw a line passing through these two points to graph the equation.
2. Graph of y = x + 5:
This equation is already in slope-intercept form, where the slope is 1 (coefficient of x) and the y-intercept is 5.
Now, we'll draw a line with a slope of 1 passing through the point (0, 5).
Now, we can see that the two lines intersect at the point (2, 7). This means that this point is the solution to both equations.
To verify the solution:
When x = 2, y = 2 + 5 = 7.
Substitute these values into both equations:
4(2) + 3(7) = 8 + 21 = 29
2 + 5 = 7
Therefore, the solution to the system of equations is x = 2 and y = 7.