Answer:
Solution: [tex]x=4[/tex], [tex]y = \frac{5}{2}[/tex]
Step-by-step explanation:
System of Equations
Solve the system:
x + 4y = 14
3x - 2y = 7
using the elimintation method.
To use the elimination method, we must add or subtract both equations in such a way that one of the variables goes away, and only one remains.
It requires to multiply one of them by a specific factor to match the coefficients. For example, multiply the first equation by -3:
-3x - 12y = -42
And add it to the second:
3x - 2y = 7
To result:
-14y = -35
Divide by -14:
[tex]y = -35/(-14)[/tex]
Simplifying:
[tex]y = \frac{5}{2}[/tex]
Now calculate x:
[tex]x = 14 - 4*\frac{5}{2}[/tex]
[tex]x = 14-10[/tex]
[tex]x=4[/tex]
Solution: [tex]x=4[/tex], [tex]y = \frac{5}{2}[/tex]
