3a + 2b = 24
4a + 5b = 53
To use the addition method, we can multiply the first equation by 5 and the second equation by -2 to get b-terms with opposite coefficients:
5(3a + 2b = 24) --> 15a + 10b = 120
-2(4a + 5b = 53) --> -8a -10b = -106
Add the equations together and the b-terms cancel out:
15a + 10b = 120
-8a - 10b = -106
+_____________
7a = 14
a = 2
To find b, substitute back using a:
3(2) + 2b = 24
6 + 2b = 24
2b = 18
b = 9
Finally, we must be sure to check our work by substituting back:
3(2) + 2(9) = 24 --> 6 + 18 = 24 <--True
4(2) + 5(9) = 53 --> 8 + 45 = 53 <--True
Answer:
a = 2
b = 9
