Ans: 4/10 8. Solve the following system of linear equations: 3x+y=10 x−y=2 Ans: x=3 y=1 $
(system of equations, linear equations, substitution method, elimination method)
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Step-by-Step Solution
Step 1: Add the two equations
We have two linear equations. We can solve this system using the elimination method. Notice that the coefficients of y are +1 and −1. Adding the two equations will eliminate the y variable, allowing us to solve for x.
Step 2: Simplify and solve for x
After adding the equations, the y terms cancel out, leaving us with an equation involving only x. We then simplify this equation to find the value of x.
Step 3: Substitute x into an equation
Now that we have the value of x, we can substitute it into either of the original equations to find the value of y. Let's use the first equation, 3x+y=10.
Step 4: Solve for y
By substituting x=3 into the first equation, we get 9+y=10. Subtracting 9 from both sides gives us the value of y.