use substitution to solve the system 2x-y=-4 -3x+y=-9
2x - y = -4
-3x + y = -9
From the first equation:
y = 2x + 4
Substitute this into the second equation:
-3x + 2x + 4 = -9
-x + 4 = -9
-x = -13
x = 13
Then plug this answer back into the first equation
2*13 - y = -4
26 - y = -4
-y = -30
y = 30
To solve the given system of equations using the substitution method, we'll start by solving one equation for one variable and substituting it into the other equation.
Let's solve the first equation, 2x - y = -4, for y:
y = 2x + 4.
Now, substitute this expression for y in the second equation:
-3x + (2x + 4) = -9.
Combine like terms:
-3x + 2x + 4 = -9,
-x + 4 = -9.
Subtract 4 from both sides:
-x = -13.
Divide by -1:
x = 13.
Substitute this value back into the first equation to find y:
2(13) - y = -4,
26 - y = -4.
Subtract 26 from both sides:
-y = -30.
Divide by -1:
y = 30.
So, the solution to the system of equations is x = 13 and y = 30.
To solve the system of equations using the substitution method, you need to follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, 2x - y = -4, for y:
y = 2x + 4.
Step 2: Substitute the expression obtained in step 1 into the other equation.
Substitute y = 2x + 4 into the second equation, -3x + y = -9:
-3x + (2x + 4) = -9.
Step 3: Simplify and solve for x.
Start by removing parentheses:
-3x + 2x + 4 = -9.
Combine like terms:
-x + 4 = -9.
Subtract 4 from both sides:
-x = -9 - 4,
-x = -13.
Multiply both sides by -1 to isolate x:
x = 13.
Step 4: Substitute the value of x back into one of the original equations to find y.
Let's use the first equation, 2x - y = -4:
2(13) - y = -4,
26 - y = -4.
Subtract 26 from both sides:
-y = -4 - 26,
-y = -30.
Multiply both sides by -1 to isolate y:
y = 30.
So the solution to the system of equations is x = 13 and y = 30.