Solving with Elimination Quick Check
4 of 54 of 5 Items
Question
Solve the system of equations.
3x−4y=40
5x−5y=55(1 point)
Responses
(8,−3)
left parenthesis 8 comma negative 3 right parenthesis
(18, 7)
left parenthesis 18 comma 7 right parenthesis
(14, 3)
left parenthesis 14 comma 3 right parenthesis
(4,−7)
left parenthesis 4 comma negative 7 right parenthesis
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To solve this system of equations using elimination, we can multiply the first equation by 5 and the second equation by 4 to make the coefficients of y equal and then subtract the equations to eliminate y:
Equation 1: 3x - 4y = 40
Equation 2: 5x - 5y = 55
Multiply Equation 1 by 5:
15x - 20y = 200
Multiply Equation 2 by 4:
20x - 20y = 220
Subtract the two equations:
15x - 20y - (20x - 20y) = 200 - 220
-5x = -20
x = 4
Now, plug the value of x back into one of the original equations to solve for y:
3(4) - 4y = 40
12 - 4y = 40
-4y = 28
y = -7
Therefore, the solution to the system of equations is (4, -7).