Solve the following algebraically
X+2y=17
X-y=2 can you pls leave the steps of how to complete this problem
come on, this is just Algebra I all over again.
From the first equation, x = 17-2y
Plug that into the 2nd equation and you have
17-2y-y=2
-3y=-15
y=5
Or, from the 2nd equation, x=y+2, so
y+2+2y=17
3y=15
y=5
Or, just subtract the 2nd from the first, and you get
3y=15
y=5
In any case, now you can easily find x.
To solve the given system of equations algebraically:
Step 1: Start by eliminating one variable. In this case, we can eliminate the variable "x" by multiplying the second equation by 2.
Equation 1: x + 2y = 17
Equation 2: 2(x - y) = 2
Step 2: Expand and simplify Equation 2:
2x - 2y = 4
Step 3: Rewrite the equations:
Equation 1: x + 2y = 17
Equation 3: 2x - 2y = 4
Step 4: Add Equation 1 and Equation 3:
(x + 2y) + (2x - 2y) = 17 + 4
3x = 21
Step 5: Divide both sides of the equation by 3 to isolate x:
3x/3 = 21/3
x = 7
Step 6: Substitute x = 7 into any of the original equations. Let's use Equation 1:
7 + 2y = 17
Step 7: Solve for y:
2y = 17 - 7
2y = 10
y = 10/2
y = 5
Step 8: The solution to the system of equations is x = 7 and y = 5.
To solve this system of equations algebraically, you can use the method of substitution. Here are the steps:
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation, X - y = 2, for X:
X = y + 2
Step 2: Substitute the expression for X in terms of y from step 1 into the other equation. Substituting X = y + 2 into the first equation, we get:
(y + 2) + 2y = 17
Step 3: Simplify the equation by combining like terms:
3y + 2 = 17
Step 4: Solve for y by isolating the variable. Subtract 2 from both sides of the equation:
3y = 15
Step 5: Divide both sides of the equation by 3 to solve for y:
y = 5
Step 6: Substitute the value of y into either of the original equations to solve for X. Let's use the first equation, X + 2y = 17:
X + 2(5) = 17
X + 10 = 17
Step 7: Solve for X by subtracting 10 from both sides of the equation:
X = 7
The solution to the system of equations is X = 7 and y = 5.