How would you solve each system by the substitution method?
1. Y=6x-5
Y=-x+9
well, we know that both are y so
6x-5 = -x+9
7 x = 14
x = 2
then y = -x+9 = -2+9 = 7
I still don't get it.
To solve this system of equations using the substitution method, we need to solve one equation for one variable and substitute it into the other equation. Let's solve equation 2 for y and substitute it into equation 1.
Equation 2: Y = -x + 9
Step 1: Solve equation 2 for y
Rearrange equation 2 to solve for y:
y = -x + 9
Step 2: Substitute the value of y from equation 2 into equation 1
Replace the y in equation 1 with the expression -x + 9:
Y = 6x - 5
6x - 5 = -x + 9
Step 3: Solve for x
Combine like terms by moving all the terms with x to one side of the equation:
6x + x = 9 + 5
7x = 14
Divide both sides of the equation by 7 to isolate x:
x = 2
Step 4: Substitute the value of x back into equation 2 to find y
Substitute x = 2 into equation 2:
y = -x + 9
y = -(2) + 9
y = -2 + 9
y = 7
So the solution to the system of equations is x = 2 and y = 7.