y=3x + 13
y=7x + 17
Solving Equations using Elimination
subtract the two as they stand
0 = 4x + 4
4x = -4
x = -1, sub into either of the two originals to get y
To solve the given system of equations using elimination, we need to eliminate one variable by manipulating the equations. Here's how we can do it step-by-step:
Step 1: Write down the given equations.
y = 3x + 13 ---(Equation 1)
y = 7x + 17 ---(Equation 2)
Step 2: Choose a variable to eliminate. In this case, let's eliminate the variable "y".
Step 3: Multiply the two equations by suitable constants so that the coefficients of "y" in both equations are the same. We can achieve this by multiplying Equation 1 by 7 and Equation 2 by 3.
7(y) = 7(3x + 13) ---(Equation 1 multiplied by 7)
3(y) = 3(7x + 17) ---(Equation 2 multiplied by 3)
Step 4: Simplify the equations obtained in Step 3.
7y = 21x + 91 ---(Equation 3)
3y = 21x + 51 ---(Equation 4)
Step 5: Now, we subtract Equation 4 from Equation 3 to eliminate "y" and solve for "x".
7y - 3y = (21x + 91) - (21x + 51)
4y = 40
y = 40/4
y = 10
Step 6: Substitute the value of "y" back into one of the original equations (either Equation 1 or Equation 2) to solve for "x".
y = 3x + 13
10 = 3x + 13
3x = 10 - 13
3x = -3
x = -3/3
x = -1
Step 7: The solution to the given system of equations is x = -1 and y = 10.
So, the solution to the given system of equations using elimination is x = -1 and y = 10.
To solve the system of equations using elimination, we want to eliminate one variable by manipulating the equations in a way that results in an equal coefficient for that variable in both equations. In other words, we want to make the coefficients of either x or y equal in both equations.
Let's solve the given system of equations using elimination:
Step 1: Multiply the first equation by 7 and the second equation by 3. This will allow us to have equal coefficients for x in both equations.
7(y) = 7(3x + 13) becomes 7y = 21x + 91
3(y) = 3(7x + 17) becomes 3y = 21x + 51
Step 2: Now, we have equal coefficients for x in both equations. Subtract the second equation from the first equation to eliminate x.
7y - 3y = (21x + 91) - (21x + 51)
Simplifying, we get 4y = 40
Step 3: Divide both sides of the equation by 4 to solve for y.
4y/4 = 40/4
y = 10
Step 4: Now substitute the value of y into either of the original equations to solve for x.
y = 3x + 13
10 = 3x + 13
Subtract 13 from both sides:
10 - 13 = 3x
-3 = 3x
Divide both sides by 3:
-3/3 = x
x = -1
So, the solution to the system of equations is x = -1 and y = 10.