Question

Multiply each equation by a number that producess opposite coefficients for x and y?

4x+5y=7

3x-2y=-12
(number between =5 and 5 for both)

Answer 1

Let's solve your system by substitution.

3x−2y=−12;4x+5y=7

Step: Solve3x−2y=−12for x:

3x−2y=−12

3x−2y+2y=−12+2y(Add 2y to both sides)

3x= 2y−12

3 3

=

2y−12

3

(Divide both sides by 3)

x=

2

3 y−4

Step: Substitute

2

3

y−4 for x in 4x+5y=7:

4x+5y=7

4( 2/3 y−4)+5y=7

23

3

y−16=7(Simplify both sides of the equation)

23

3

y−16+16=7+16(Add 16 to both sides)

23

3

y=23

23

3 y

23

3 = 23

23

3

(Divide both sides by 23/3)

y=3

Step: Substitute 3 for y in x=

2

3 y−4:

x=

2

3 y−4

x= 2

3 (3)−4

x=−2(Simplify both sides of the equation)

Answer:

x=−2 and y=3 (underlined and / are fractions or division)