Answer:
[tex]x=3,\ \ y=-1[/tex]
Step-by-step explanation:
We have the following two equations:
[tex]3x+2y=7[/tex]
[tex]2x-5y=11[/tex]
To solve the system by the elimination method multiply the first equation by [tex]\frac{5}{2}[/tex] and add it to the second equation
By multiplying the first equation by [tex]\frac{5}{2}[/tex] you get the following:
[tex]\frac{15}{2}x+5y=\frac{35}{2}[/tex]
Now we add the two equations
[tex]\frac{15}{2}x+5y=\frac{35}{2}[/tex]
[tex]2x-5y=11[/tex]
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[tex]\frac{19}{2}x=\frac{57}{2}\\\\19x=57\\\\x=\frac{57}{19}\\\\x=3[/tex]
Now substitute the value of x in either equation and solve for y
[tex]2(3)-5y=11[/tex]
[tex]6-5y=11[/tex]
[tex]-5y=11-6[/tex]
[tex]-5y=5[/tex]
[tex]y=-1[/tex]
