Solve the system using substitution. y=8-x 7=2-y
Eq1: y = 8-x.
Eq2: 7 = 2 - y.
Solve Eq2 for Y:
Y = 2-7 = -5.
In Eq1, replace Y with -5 and solve for X.
To solve the system of equations using substitution, we will replace one variable in one equation with an expression involving the other variable, and then substitute this expression into the other equation. Let's solve the system of equations step-by-step:
Step 1: Start with the given system of equations:
y = 8 - x .................(Equation 1)
7 = 2 - y .................(Equation 2)
Step 2: Solve Equation 1 for y:
y = 8 - x
Step 3: Substitute the expression for y from Equation 1 into Equation 2:
7 = 2 - (8 - x)
Now, let's simplify Equation 2:
Step 4: Remove the parentheses:
7 = 2 - 8 + x
Step 5: Combine like terms:
7 = -6 + x
Step 6: Solve for x:
Add 6 to both sides:
7 + 6 = x
13 = x
Step 7: Substitute the value of x into Equation 1 to solve for y:
y = 8 - x
y = 8 - 13
y = -5
Step 8: The solution to the system of equations is:
x = 13
y = -5
Therefore, the solution to the given system of equations using substitution is x = 13, y = -5.
y=8-x
7=2-y
How do you think you should solve this?