i need help with this problem:2x-y=-4
-x-y=5
when you answer this question can you plz include the steps you did to get the final answer?
A way to solve this type of problem:
First express one of the variables in terms of the other.
-x-y = 5
or, y = -5-x
Now substitute that value for y into the other equation.
2x -(-5-x)=-4
Solve for x, then substitute the known x value into either equation to solve for y.
Subtract the second equation from the first.
3x = -9
x = -3
y = -x -5 = -2
Sure! To solve this system of equations, we can use the method of elimination. Here are the steps:
Step 1: Multiply the second equation by 2 to make the coefficients of x in both equations equal:
2(-x - y) = 2(5)
-2x - 2y = 10
Step 2: Now, we have two equations:
2x - y = -4
-2x - 2y = 10
Step 3: Add the two equations together to eliminate the x term:
(2x - y) + (-2x - 2y) = -4 + 10
2x - y - 2x - 2y = 6 - in this step, 2x and -2x cancel out, and -y and -2y add together to give -3y
Step 4: Simplify the equation:
-3y = 6
Step 5: Solve for y by dividing both sides of the equation by -3:
-3y / -3 = 6 / -3
y = -2
Step 6: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
2x - (-2) = -4 - here, we substitute -2 for y
2x + 2 = -4
Step 7: Solve for x by subtracting 2 from both sides of the equation:
2x = -4 - 2
2x = -6
Step 8: Divide both sides of the equation by 2 to isolate x:
2x / 2 = -6 / 2
x = -3
Step 9: The solution to the system of equations is x = -3, y = -2.
So, the final answer is x = -3 and y = -2.