To solve the system of equations using elimination, we will multiply the first equation by 4 and the second equation by 3 to make the coefficient of y the same:
4(2x-3y)=-4(-1)
3(3x+4y)=3(7)
Simplifying, we get:
8x-12y=4
9x+12y=21
Now we eliminate the variable y by adding the two equations:
(8x-12y)+(9x+12y)=4+21
Combining like terms, we get:
17x=25
To solve for x, divide both sides of the equation by 17:
17x/17=25/17
Simplifying, we get:
x=25/17
Now we substitute this value of x back into one of the original equations to solve for y. Let's use the first equation:
2(25/17)-3y=-1
Multiplying through by 17 to get rid of the fraction, we get:
50-51y=-17
Subtracting 50 from both sides, we get:
-51y=-67
Dividing by -51, we get:
y=(-67)/(-51)
Simplifying, we get:
y=67/51
Thus, the solution to the system of equations is:
x = 25/17
y = 67/51
solve the system using elimination
2x-3y=-1
3x+4y=7
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