System of equations:
• Equation 1
[tex]5x+2y=-7[/tex]
• Equation 2
[tex]5x+3y=2[/tex]
Procedure
This system is easier if we solve it using the elimination method, in which we multiply the first equation times minus one, add both equations to eliminate the x variable, and solve for y.
0. Multiplying Equation 1 times minus 1.
[tex]-1\cdot(5x+2y=-7)[/tex][tex]-5x-2y=7[/tex]
2. Adding both equations:
[tex]\begin{gathered} -5x-2y=7 \\ +(5x+3y=2) \\ --------- \\ 0+1\cdot y=9 \end{gathered}[/tex]
Then:
[tex]y=9[/tex]
3. Finally, substituting this value in any equation and solving for x:
[tex]5x+2\cdot9=-7[/tex][tex]5x+18=-7[/tex][tex]5x=-7-18[/tex][tex]x=-\frac{25}{5}=-5[/tex]
Answer: y = 9 and x = -5.
