Solve by Addition/Elimination -3x+2y=10 , 4x-7y=4

Problem

{[−3*x+2*y=10],[4*x−7*y=4])

Solution

1. Multiply the first equation by 4 and the second equation by 3 to make the coefficients of x opposites.

4*(−3*x+2*y)=4*(10)⇒−12*x+8*y=40

3*(4*x−7*y)=3*(4)⇒12*x−21*y=12

2. Add the two resulting equations together to eliminate the x variable.

(−12*x+12*x)+(8*y−21*y)=40+12

−13*y=52

3. Solve for y by dividing both sides by −13

y=52/(−13)

y=−4

4. Substitute the value of y back into the first original equation to find x

−3*x+2*(−4)=10

−3*x−8=10

5. Isolate the x term by adding 8 to both sides.

−3*x=18

6. Solve for x by dividing both sides by −3

x=18/(−3)

x=−6

Final Answer

(x,y)=(−6,−4)

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