5y+3x=15
−2y−4x=−34
To solve the given system of equations using the elimination method, we proceed as follows:
Step 1: Align the equations to eliminate one variable.
We have: 5y+3x−2y−4xamp;=15(Equation 1)amp;=−34(Equation 2)
Step 2: Make the coefficients of y equal in magnitude by manipulating the equations.
Multiply Equation 1 by 2 and Equation 2 by 5:
(2)⋅(5y+3x)(5)⋅(−2y−4x)amp;=2⋅15⇒10y+6x=30amp;=5⋅(−34)⇒−10y−20x=−170
Step 3: Add the modified equations to eliminate y.
(10y+6x)+(−10y−20x)0y−14x−14xamp;=30+(−170)amp;=−140amp;=−140
Step 4: Solve for x.
Dividing by −14:
xxamp;=−14−140amp;=10
Step 5: Substitute x=10 back into one of the original equations to solve for y.
Using Equation 1:
5y+3(10)5y+305y5yyyamp;=15amp;=15amp;=15−30amp;=−15amp;=5−15amp;=−3
Therefore, the solution to the system of equations is x=10 and y=−3.
x=10,y=−3