Question

Solve the system of equations by multiplying. -3x +2y= 4 4x-13y=5

Answer 1

x=-2 and y=-1

Explanation:

To find the value of x and y, isolate it on one side of the equation.

-3x+2y=4, 4x=13y=5

-3x+2y=4

`\rightarrow \sf{x=-(4-2y)/(3)}`

Substitute.

`\sf{4\left(-(4-2y)/(3)\right)-13y=5}`

Solve.

Use the distributive property.

A(B+C)=AB+AC

A(B-C)=AB-AC

`\sf{=(-16-31y)/(3)=5}`

Isolate the term of y.

Multiply by 3 from both sides.

`\sf{(3\left(-16-31y\right))/(3)=5*3}`

Solve.

Multiply the numbers from left to right.

5*3=15

-16-31y=15

Add by 16 from both sides.

-16-31y+16=15+16

Solve.

15+16=31

-31y=31

Divide by -31 from both sides.

-31y/-31=31/-31

Solve.

y=-1

Substitute of y=-1.

`\sf{x=-(4-2\left(-1\right))/(3)}`

Solve.

Use the order of operations.

PEMDAS stands for:

• Parentheses
• Exponents
• Multiply
• Divide
• Add
• Subtract

4-2(-1)

Do parentheses by multiply first.

2(-1)=-2

4-(-2)

4+2=6

-6/3

Divide.

-6/3=-2

x=-2

`\Rightarrow \boxed{\sf{x=-2, \quad y=-1}}`

Therefore, the correct answer is x=-2, and y=-1.

I hope this helps, let me know if you have any questions.