elimination method 4p+3q=6 and 3p-5q=-10
multiply the equations by factors to equalize the p or q coefficients between the equations
then add or subtract the resulting equations to eliminate p or q
solve for the variable , then substitute back to find the other variable
like:
3(4p+3q=6) and 4(3p-5q=-10 )
is
12 p + 9 q = +18
12 p - 29 q = -40
----------------------- subtract
To solve the system of equations using the elimination method, the goal is to eliminate one variable by adding or subtracting the equations.
Let's start by multiplying the first equation by 3 and the second equation by 4 to make the coefficients of the "p" terms equal:
3 * (4p + 3q) = 3 * 6
4 * (3p - 5q) = 4 * (-10)
Simplifying these equations, we get:
12p + 9q = 18
12p - 20q = -40
Now, subtracting the second equation from the first equation to eliminate the "p" terms:
(12p + 9q) - (12p - 20q) = 18 - (-40)
Simplifying, we have:
12p + 9q - 12p + 20q = 18 + 40
29q = 58
To solve for q, divide both sides of the equation by 29:
q = 58 / 29
q = 2
Now substitute the value of q back into one of the original equations. Let's use the first equation, with p and q as variables:
4p + 3q = 6
4p + 3(2) = 6
4p + 6 = 6
Subtracting 6 from both sides:
4p = 0
Dividing by 4, we find:
p = 0
Therefore, the solution to the system of equations is p = 0 and q = 2.