Solve by the elimination method.
9x−
y=
11
x+3y=
23
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Please put equation all on one line.
9x - y = 11
x + 3y = 23
Multiply first equation by 3.
27x - 3y = 33
Add second and third equation to solve for x. Then solve for y by inserting x value into one of the two top equations.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant to make the coefficients of one of the variables the same in both equations. In this case, let's eliminate the variable "y" by making the coefficients the same.
Multiply Equation 1 by 3, giving you:
27x - 3y = 33
Now the coefficients of "y" in both equations are the same (both -3y).
Step 2: Subtract the two equations to eliminate one variable.
(27x - 3y) - (x + 3y) = 33 - 23
Simplifying, you get:
27x - 3y - x - 3y = 10
26x - 6y = 10
Step 3: Now, solve this new equation for "x".
26x - 6y = 10
Step 4: Divide through the equation by the coefficient of "x" (26) to isolate "x".
x - (6/26)y = 10/26
x - (3/13)y = 5/13
Step 5: Now, solve Equation 2 for "x".
x + 3y = 23
Isolate "x":
x = 23 - 3y
Step 6: Now that you have both equations in terms of "x", set them equal to each other.
23 - 3y = 5/13 - (3/13)y
To solve for "y", move all terms with "y" to the left side:
(3/13)y - (3/13)y = 23 - 5/13
0y = (299/13) - (5/13)
0y = (294/13)
Since any number multiplied by 0 is 0, "y" can be any value.
Step 7: To find "x", substitute the value of "y" back into either original equation.
Let's substitute it into Equation 2:
x + 3(0) = 23
x + 0 = 23
x = 23
Therefore, the solution to the system of equations is x = 23 and y is any value.