Final answer:
To solve the system of linear equations by elimination, multiply the second equation by a suitable constant and then add it to the first equation. Substitute the value of y into the second equation to solve for x. The solution to the system of linear equations is x = -100/9 and y = 38/9.
Step-by-step explanation:
To solve the system of linear equations by elimination, we need to eliminate one of the variables by multiplying one or both of the equations by suitable constants. Let's start by multiplying the second equation by 2:
2*(-x+4y) = 2*28
-2x+8y = 56
Now, we can add this equation to the first equation:
(2x+10y)+ (-2x+8y) = 20+56
18y = 76
y = 76/18
y = 38/9
Substituting this value of y into the second equation:
-x+4*(38/9) = 28
-x+152/9 = 28
-x = 28-152/9
-x = 252/9-152/9
-x = 100/9
x = -100/9
Therefore, the solution to the system of linear equations is:
x = -100/9
y = 38/9