Solve the system using elimination. 3x+2y=17 2x+5y=26 (1 point) Responses - image with description: the ordered pair (3, 4) - - no response given - image with description: the ordered pair (2, 11 over 2) - - no response given - image with description: the ordered pair (one-half, 5) - - incorrect
To solve the system of equations using elimination, we can choose to eliminate either the x or the y term by multiplying the equations by appropriate constants.
Multiplying the first equation by 2 and the second equation by 3 will allow us to cancel out the y terms:
(2)(3x+2y) = (2)(17) -> 6x + 4y = 34
(3)(2x+5y) = (3)(26) -> 6x + 15y = 78
Subtracting the first equation from the second equation will cancel out the x terms:
(6x + 15y) - (6x + 4y) = 78 - 34
11y = 44
y = 4
Substituting this value of y into the first equation:
3x + 2(4) = 17
3x + 8 = 17
3x = 9
x = 3
Therefore, the system of equations is solved by the ordered pair (3,4).