Solve system by substitution or elimination x+4y=13
2x+3y=6
substitution:
x = 13-4y, so
2x+3y = 2(13-4y)+3y = 6
26-8y+3y = 6
-5y = -20
y = 4
so, x=13-4y=13-4*4 = -3
Elimination:
Multiply the 1st equation by 2, and you get
2x+8y=26
2x+3y=6
Now subtract and you have
5y=20
and so on as above,
To solve the given system of equations:
Step 1: Choose a method (substitution or elimination) to solve the system. Both methods are viable, so we'll use the elimination method in this example.
Step 2: Rearrange one or both equations, if necessary, so that the coefficients of one variable match. In this case, we'll eliminate the x variable by multiplying the first equation by 2 and the second equation by -1:
Equation 1: 2(x + 4y) = 2(13) => 2x + 8y = 26
Equation 2: -1(2x + 3y) = -1(6) => -2x - 3y = -6
Step 3: Add the revised equations together, eliminating the x variable:
(2x + 8y) + (-2x - 3y) = 26 + (-6)
8y - 3y = 20
5y = 20
Step 4: Solve for y by dividing both sides of the equation by 5:
5y/5 = 20/5
y = 4
Step 5: Substitute the value of y (y = 4) into one of the original equations and solve for x. Using the first equation:
x + 4y = 13
x + 4(4) = 13
x + 16 = 13
x = 13 - 16
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 4.
To solve the system of equations by substitution or elimination, we need to eliminate one variable and solve for the other.
Let's start by solving the first equation for x:
x + 4y = 13
x = 13 - 4y (Subtract 4y from both sides)
Now substitute this expression for x into the second equation:
2x + 3y = 6
2(13 - 4y) + 3y = 6 (Substitute the value of x)
Now simplify and solve for y:
26 - 8y + 3y = 6 (Distribute 2 to each term inside the parentheses)
-8y + 3y = 6 - 26 (Combine like terms)
-5y = -20 (Combine the constants)
y = 4 (Divide both sides by -5)
Now substitute the value of y back into the first equation to solve for x:
x + 4(4) = 13 (Substitute the value of y)
x + 16 = 13 (Multiply 4 by 4)
x = 13 - 16 (Subtract 16 from both sides)
x = -3
So the solution to the system of equations is x = -3 and y = 4.