Question

x+3.5y=9.5
2x+2y=14
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Answer 1

To solve this system of equations, we can use the method of substitution or elimination.

Method of substitution:
1) Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:
x = 9.5 - 3.5y

2) Substitute the value of x into the second equation:
2(9.5 - 3.5y) + 2y = 14

3) Simplify and solve for y:
19 - 7y + 2y = 14
-5y = 14 - 19
-5y = -5
y = -5 / -5
y = 1

4) Substitute the value of y into the first equation to solve for x:
x + 3.5(1) = 9.5
x + 3.5 = 9.5
x = 9.5 - 3.5
x = 6

5) The solution to the system of equations is x = 6 and y = 1.

Method of elimination:
1) Multiply the first equation by 2 to eliminate the x-term in the second equation:
2(x + 3.5y) = 2(9.5)
2x + 7y = 19

2) Subtract the second equation from the equation obtained in the previous step:
(2x + 7y) - (2x + 2y) = 19 - 14
5y = 5
y = 5 / 5
y = 1

3) Substitute the value of y into the first equation to solve for x:
x + 3.5(1) = 9.5
x + 3.5 = 9.5
x = 9.5 - 3.5
x = 6

4) The solution to the system of equations is x = 6 and y = 1.

Therefore, the solution to the given system of equations is x = 6 and y = 1.