Solve by elimination method.
2r-5s=-33
5r+2s=48
can someone please check my answer?
the answer I got was s= -69/-21 or 3.28
I didn't get that. Did you separate one of the variables by itself then plug it into the other equation? It has to be r= not 2r= or anything
hmmm this is where I get confused which variable do I need to multiply to eliminate...
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply the equations by suitable constants to make the coefficients of one of the variables in each equation opposite in sign. This allows you to add or subtract the equations to eliminate that variable.
In this case, you can multiply the first equation by 5 and the second equation by 2 to make the coefficients of 's' opposite:
Equation 1: (5)(2r) - (5)(5s) = (5)(-33)
Simplified: 10r - 25s = -165
Equation 2: (2)(5r) + (2)(2s) = (2)(48)
Simplified: 10r + 4s = 96
Step 2: Now we can add the equations together. By doing this, the variables 'r' will be eliminated.
(10r - 25s) + (10r + 4s) = -165 + 96
20r - 21s = -69
Step 3: Now we have a new equation with only the variable 's'. Simplify it further:
20r - 21s = -69
Step 4: Rearrange the equation to solve for 's':
-21s = -69 - 20r
s = (-69 - 20r)/(-21)
s = (69 + 20r)/21
Step 5: Substitute this value for 's' into one of the original equations. Let's use the first equation:
2r - 5((69 + 20r)/21) = -33
Step 6: Solve for 'r':
Multiply every term of the equation by 21 to eliminate the fraction:
42r - 115(69 + 20r) = -693
Simplify:
42r - 115(69) - 115(20r) = -693
42r - 7955 - 2300r = -693
Collect like terms:
42r - 2300r = -693 + 7955
-2258r = 7262
Divide both sides by -2258:
r = 7262 / -2258
r ≈ -3.214
Step 7: Substitute the value of 'r' back into one of the original equations to find 's'. Let's use the first equation:
2(-3.214) - 5s = -33
-6.427 - 5s = -33
-5s = -33 + 6.427
-5s = -26.573
Divide both sides by -5:
s = -26.573 / -5
s ≈ 5.315
Therefore, the solution to the system of equations is:
r ≈ -3.214
s ≈ 5.315