solve the system of equations using the substitution method.
y=2x-5
3x+4y=-9
correct, your work should look something like this:
y=2x-5
3x+4y=-9
sub the value of y from the first into the second:
3x + 4(2x-5) = -9
3x + 8x - 20 = -9
11x = 11
x = 1
sub x = 1 back into the first
y = 2(1) - 5)
= 2 - 5
= -3
is (1,-3) correct
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
In this case, we'll solve the first equation, y = 2x-5, for y.
y = 2x - 5
Step 2: Substitute the expression found in step 1 into the second equation.
Replace y in the second equation, 3x + 4y = -9, with 2x - 5:
3x + 4(2x - 5) = -9
Step 3: Simplify and solve the resulting equation for x.
Distribute 4 into the parentheses:
3x + 8x - 20 = -9
Combine like terms:
11x - 20 = -9
Add 20 to both sides of the equation:
11x = 11
Divide both sides by 11:
x = 1
Step 4: Substitute the value of x back into one of the original equations and solve for y.
Using the first equation, y = 2x - 5:
y = 2(1) - 5
y = 2 - 5
y = -3
Step 5: Write the solution as an ordered pair (x, y).
The solution to the system of equations is (1, -3).