How would you solve this system?
Y=-x+3
Y=x+4
3/4
if y = -x+3 and y = x+4
then
x+4 = -x + 3
2x =-1
x = -1/2
and y = -1/2 + 4 = 7/2
To solve this system of equations, you can use the method of substitution.
Step 1: Start with the first equation, Y = -x + 3.
Step 2: Substitute the value of Y from the second equation into the first equation. Since the second equation is Y = x + 4, substitute (x + 4) in place of Y in the first equation.
So, the first equation becomes: (x + 4) = -x + 3.
Step 3: Now, solve the equation for x. Start by simplifying both sides.
Combine like terms: x + 4 = -x + 3.
Step 4: Add x to both sides to isolate the variable x.
x + x + 4 = -x + x + 3.
Simplify: 2x + 4 = 3.
Step 5: Subtract 4 from both sides to isolate the variable x.
2x + 4 - 4 = 3 - 4.
Simplify: 2x = -1.
Step 6: Divide both sides by 2 to solve for x.
(2x)/2 = (-1)/2.
Simplify: x = -1/2.
Step 7: Now that you have the value of x, substitute it back into either of the original equations to find the value of Y.
Using the second equation Y = x + 4, substitute x = -1/2.
Y = (-1/2) + 4.
Simplify: Y = 3.5.
So, the solution to the system of equations is x = -1/2 and Y = 3.5.