use substitution to solve the system
-5x+2y=27
y=2x+11
x=
y=
Use substitution means replace y in the first equation with what y equals in terms of x.
-5x + 2(2x+11) = 27
Next, multiply by 2 to remove ( )
combine like terms
continues to solve for x.
Find y by replacing x with your answer for x in y = 2x+11
Always...check x and y in both equations.
To solve the system of equations using substitution, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
In this case, the second equation is already solved for y.
The second equation is:
y = 2x + 11
Step 2: Substitute the expression for the variable in the other equation.
Substitute the expression for y (2x + 11) into the first equation:
-5x + 2(2x + 11) = 27
Step 3: Simplify and solve for x.
Distribute 2 into the parentheses:
-5x + 4x + 22 = 27
Combine like terms:
-x + 22 = 27
Subtract 22 from both sides:
-x = 5
Multiply both sides by -1 to isolate x:
x = -5
Step 4: Substitute the value of x back into one of the original equations to find y.
Let's substitute x = -5 into the second equation:
y = 2(-5) + 11
y = -10 + 11
y = 1
So the solutions to the system of equations are:
x = -5
y = 1