Solve the linear system by using elimination.
9x-4y=26
18x+7y=22
multiply the top by 2:
18x - 8y = 52
18x + 7y = 22
subtract:
15y = -30
y = -2
so
x = 2
To solve the linear system using elimination, we need to eliminate one variable by multiplying one or both equations by appropriate factors such that when we add the equations together, one of the variables is eliminated.
Let's start by eliminating the variable "y". We can do this by multiplying the first equation by 7 and the second equation by 4. This will give us:
(7 * 9x) - (7 * 4y) = 7 * 26
(4 * 18x) + (4 * 7y) = 4 * 22
Simplifying these equations, we get:
63x - 28y = 182
72x + 28y = 88
Now, add the two equations together:
(63x - 28y) + (72x + 28y) = 182 + 88
Simplifying this equation, we get:
63x - 28y + 72x + 28y = 270
Combine like terms:
135x = 270
Divide both sides by 135:
x = 2
Now that we have the value of x, substitute it back into either of the original equations to find the value of y. Let's use the first equation:
9x - 4y = 26
Substituting x = 2:
9(2) - 4y = 26
18 - 4y = 26
Subtract 18 from both sides:
-4y = 8
Divide both sides by -4:
y = -2
Therefore, the solution to the linear system is x = 2 and y = -2.