Solve the following system of equations:
{−8x+5y=310x+y=16
To solve this system of equations, we will use the elimination method.
The system of equations is:
{−8x+5y=310x+y=16
We will first make the coefficients of y the same so that we can eliminate y. To do that, we need both equations to have the same coefficient for y. The first equation already has 5y, so we will multiply the second equation by 5:
5(10x+y)=5×16
This gives the equation:
50x+5y=80
Now the system is:
{−8x+5y=350x+5y=80
We will subtract the first equation from the second to eliminate y:
(50x+5y)−(−8x+5y)=80−3
Solving this, we get:
50x−(−8x)+5y−5y=80−3
58x=77
Thus, the value of x is:
x=5877≈1.32
Now, we substitute this value back into one of the original equations to find y. It's often easier to substitute into the simpler equation, 10x+y=16:
10(1.32)+y=16
13.2+y=16
Solving for y, we have:
y=16−13.2=2.8
Therefore, the solution to the system of equations is:
x=1.32,y=2.8
This corresponds to the given correct answer choice.
x=1.32,y=2.8