Final answer:
To solve the first system of equations, use the method of substitution. For the second system of equations, use the method of elimination.
Step-by-step explanation:
Solving the system of equations:
To solve the system of equations 5x + y = 9 and 10x - 7y = -46, we can use the method of substitution. First, solve one equation for one variable in terms of the other variable. From the first equation, we can rearrange it to get y = 9 - 5x. Substitute this expression for y in the second equation, which gives us 10x - 7(9 - 5x) = -46. Simplify and solve for x, then substitute the value of x into one of the original equations to solve for y.
For the second system of equations -4x + 9y = 9 and x - 3y = 6, we can use the method of elimination. Multiply the second equation by 4 to eliminate the x term, giving us -4x + 9y = 9 and 4x - 12y = 24. Add the two equations together to eliminate the x term, resulting in -3y = 33. Solve for y, then substitute the value of y into one of the equations to solve for x.