Okay. So I am completely lost with this... Any help would be great!
3. Solve the system using any method – graphing, substitution, or linear combination. Make sure to show your work.
2x + 5y= 8
x + 3y= 2
Whenever you have a variable showing up as an x or y with coefficient of 1 understood, I use substitution
from the 2nd , x = 2 - 3y, now plug into the 1st
2(2-3y) + 5y = 8
4 - 6y + 5y = 8
-y = 4
y = -4
then x = 2 -3(-4) =14
x= 14 , y = -4
To solve this system of equations using the graphing method, you would follow these steps:
1. Start by labeling the two equations as Equation 1 and Equation 2.
Equation 1: 2x + 5y = 8
Equation 2: x + 3y = 2
2. Convert each equation into slope-intercept form (y = mx + b) by solving for y. Start with Equation 1:
2x + 5y = 8
5y = -2x + 8
y = (-2/5)x + 8/5
Equation 1 is now in slope-intercept form.
3. Now, convert Equation 2 into slope-intercept form:
x + 3y = 2
3y = -x + 2
y = (-1/3)x + 2/3
Equation 2 is now in slope-intercept form.
4. Graph each equation on the same coordinate plane. To do this, use the slope (m) and y-intercept (b) for each equation.
For Equation 1:
- The slope is -2/5, so from the y-intercept (8/5), move down 2 units and to the right 5 units to find another point. Plot these two points and draw a line through them.
For Equation 2:
- The slope is -1/3, so from the y-intercept (2/3), move down 1 unit and to the right 3 units to find another point. Plot these two points and draw a line through them.
5. The point where the two lines intersect is the solution to the system of equations. In this case, it looks like the lines intersect at the point (2, 0).
Therefore, the solution to the system of equations is x = 2 and y = 0.