We can solve this by substitution.
Look at the second equation. If we rearrange to find 7x, we can substitute in the value into the first equation.
[tex]5y -7x=12[/tex]
[tex]5y -7x - 12=0[/tex]
[tex]5y - 12=7x[/tex]
Therefore [tex]7x=5y-12[/tex]
Now let's replace the 7x in the first equation with 5y - 12:
[tex]2y + 7x=-5[/tex] (substitute in 7x = 5y - 12)
[tex]2y + (5y -12) =-5[/tex]
[tex]2y + 5y -12 =-5[/tex]
[tex]7y-12 =-5[/tex]
[tex]7y =7[/tex]
[tex]y =1[/tex]
Now that we know y, we can find x by substituting in y = 1 into any equation we want. I will use the equation: 7x = 5y - 12
[tex]7x=5y-12[/tex] (Substitute in y = 1)
[tex]7x=5(1)-12[/tex]
[tex]7x=5-12[/tex]
[tex]7x=-7[/tex]
[tex]x=-1[/tex]
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Answer:
[tex]y =1[/tex]
[tex]x=-1[/tex]
