Answer:
a = 4 and b = -2
Explanation:
When given 2 equations, a common question is to find values of (x,y) that satisfy both equations. In other words, do the lines intersect? The substitution method is an approach that eliminates one of the two variables (x or y) and then allows the determination of the remaining variable. That value can then be used to find the pair (x,y).
We are given 2 equations, but have two unknowns:
a + b = 2
5a - 3b = 26
Lets take the first equation and rearrange it to isolate one of the unknowns:
a + b = 2
a = 2 - b
Since a can be defined as a function of b, we can use this definition in the other equation:
5a - 3b = 26
5*(2-b) - 3b = 26 for a = (2-b)
10 - 5b - 3b = 26
-8b + 10 = 26
-8b = 16
b = -2
Use this value of b in either equation to find a:
a + b = 2
a - 2 = 2
a = 4
The point (a,b) at which these lines intersect is (4,-2)
See the attached graph (x and y are used in place of a and b)