elimination method 4p+3q=6 and 3p-5q=-1o
q=6/7
q=5
#1: 4p + 3q = 6
#2: 3p - 5q = -10
You want t get rid of either p or q, so you need to find a number that is a multiple of 4 and 3, or 3 and 5. Let's eliminate the q's. So, multiply #1 by 5, and #2 by 3. Now you have
20p + 15q = 30
9p - 15q = -30
Now if you add the two equations, the q's go away and you are left with
29p = 0
p = 0
So, now you know p=0, and you can use that in either of the original equations to determine q.
wrong answer sorry I thought there was only q's
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To solve the system of equations using the elimination method, follow these steps:
1. Multiply one or both equations by suitable numbers in order to make the coefficients of either q or p the same (but with opposite signs). In this case, we can start by multiplying the second equation by 4 to create opposite coefficients for p.
Equation 1: 4p + 3q = 6
Equation 2 (multiplied by 4): 12p - 20q = -40
2. Now, add the two equations together to eliminate one variable. In this case, by adding the equations, the p terms cancel out.
(4p + 3q) + (12p - 20q) = 6 + (-40)
16p - 17q = -34
3. Simplify the equation obtained.
16p - 17q = -34
Now we have a new equation with only one variable (q).
4. Solve for q by isolating the variable. In this case, let's solve for q by adding 17q to both sides.
16p - 17q + 17q = -34 + 17q
16p = -34 + 17q
5. Simplify the equation further.
16p = 17q - 34
6. Solve for p by dividing both sides of the equation by 16.
p = (17q - 34) / 16
Now we have expressions for both p and q. We can substitute these expressions into either of the original equations to find the values of p and q.