solve the system of equations 4x - 3y= 8 2x+ 5y= 9 mutiple choices are (1,1), (5,2) 1(-4,-10) or (2,-2)and choose the correct description of the system of equations. 2x+3y=10 and 4x+6y equals 20 thank you for the help
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To solve the system of equations 4x - 3y = 8 and 2x + 5y = 9, we can use the method of substitution or elimination.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation, 2x + 5y = 9, for x:
2x = 9 - 5y
x = (9 - 5y)/2
Step 2: Substitute the expression for x in terms of y into the other equation.
Substituting x in the first equation, we get:
4(9 - 5y)/2 - 3y = 8
Simplifying the equation:
2(9 - 5y) - 3y = 8
18 - 10y - 3y = 8
18 - 13y = 8
Step 3: Solve for y.
18 - 13y = 8
-13y = 8 - 18
-13y = -10
y = (-10)/(-13)
y = 10/13
Step 4: Substitute the value of y back into the expression for x to find x:
x = (9 - 5(10/13))/2
x = (9 - 50/13)/2
x = (117/13 - 50/13)/2
x = 67/13
Therefore, the solution to the system of equations is (x, y) = (67/13, 10/13).
As for the multiple-choice options:
(1, 1), (5, 2), (-4, -10), and (2, -2) are not the solutions to the given system of equations.
Description of the system of equations:
The system of equations 2x + 3y = 10 and 4x + 6y = 20 is a system of linear equations. The second equation is obtained by multiplying the first equation by 2. Both equations represent lines in a coordinate plane, and the solution to the system is the point of intersection of these lines.