Use the Substitution method to solve the system of equations.
x + y = -4
x - y = 2
x + y = -4
x - y = 2
In the second equation,
x= y+2 Putting that in the first..
(y+2) + y= -4
subtract two from each side, then divide each side by two to get y. Then, put that value of y into EITHER of the equations and solve for x. I will be happy to critique your thinking or work.
To solve the system of equations using the substitution method:
Step 1: Solve one of the equations for one variable in terms of the other variable.
In this case, let's solve the second equation for x:
x = y + 2
Step 2: Substitute the value of x from Step 1 into the other equation.
Substituting x = y + 2 into the first equation:
(y + 2) + y = -4
Step 3: Simplify and solve for y.
Combining like terms:
2y + 2 = -4
Subtracting 2 from both sides:
2y = -6
Dividing both sides by 2:
y = -3
Step 4: Substitute the value of y from Step 3 into either of the original equations and solve for x.
Let's substitute y = -3 into the first equation:
x + (-3) = -4
x - 3 = -4
Adding 3 to both sides:
x = -4 + 3
x = -1
Therefore, the solution to the system of equations is x = -1 and y = -3.
To solve the given system of equations using the Substitution method, we can follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable. In this case, we have the second equation:
x - y = 2
To isolate x, we can add y to both sides:
x = y + 2
Step 2: Substitute the expression for x obtained in Step 1 into the other equation. In this case, let's substitute x = y + 2 into the first equation:
x + y = -4
Replacing x with y + 2, we have:
(y + 2) + y = -4
Simplifying this equation:
2y + 2 = -4
Step 3: Solve the equation obtained in Step 2 for the variable y.
We can start by subtracting 2 from both sides:
2y = -6
Next, divide both sides by 2 to isolate y:
y = -3
Step 4: Substitute the value of y obtained in Step 3 into either of the original equations to solve for x.
Let's use the first equation: x + y = -4
Replacing y with -3, we have:
x + (-3) = -4
Simplifying:
x - 3 = -4
To isolate x, we can add 3 to both sides:
x = -1
Step 5: Check the solution by substituting the obtained values of x and y into both original equations and see if they hold true.
For the first equation:
x + y = -4
(-1) + (-3) = -4
-4 = -4 (true)
For the second equation:
x - y = 2
(-1) - (-3) = 2
2 = 2 (true)
Therefore, the solution to the given system of equations is x = -1 and y = -3.
x 4y=5
2x+8y=15
x + y = 4
2x - 3y = -2