Question

What is the solution of the system of equations?

Answer 1

Here is your system of equations:

$\left \{ {{y=-4x+10} \atop {y=-2x-6}} \right.$

When solving a system, you can either substitute, or eliminate. I am going to substitute.

In the first equation, if y is equal to -4x + 10, I can substitute the y in the second equation with -4x + 10.

Here is your new equation:

$-4x+10=-2x-6$

Since you have variables on both sides, you have to cancel it on either side. In the equation on the right, the variable is -2x. To cancel it out, you have to do the opposite of it, which is +2x, or positive 2x. That means you have to add 2x to both equations.

$-4x+10+2x = -2x-6+2x \\ \\ -2x+10=-6$

Now you have one variable and two regular integers. You have to leave the variable x alone to find its value. Along with it is +10, or positive 10. To remove it, you have to do the opposite of it, which is -10 or subtract 10.

$-2x+10-10=-6-10 \\ \\ -2x=-16$

• Remember that when you subtract from a negative number, the number will increase but the sign will stay negative.

Now you need x to stay alone, so divide both sides by -2.

$\frac{-2x}{-2}=\frac{-16}{-2} \\ \downarrow \\ x=8$

Remember:

NEGATIVES

• Negative(-) times(×) negative(-) = positive(+)

• Negative(-) times(×) positive(+) = negative(-)

• Negative(-) divided(÷) by positive(+) = negative(-)

• Negative(-) divided(÷) by negative(-) = positive(+)

POSITIVES

• Positive(+) times(×) positive(+) = positive(+)

• Positive(-) times(×) negative(-) = negative(-)

• Positive(+) divided(÷) by positive(+) = positive(+)

• Positive(+) divided(÷) by negative(-) = negative(-)

Now that you have the value of x, you can substitute it with the x in one of the equations.

$y=-4x+10 \rightarrow y=-4(8)+10$

Multiply -4 by 8:

$-4 \times 8 = -32$

Here is your new equation:

$y=-32+10$

Add -22 and 10:

$-32+10 =-22$

$\left \{ {{x=8} \atop {y=-22}} \right.$

Your answer is the third choice: (8, -22)

If you have any questions, feel free to ask in the comments! :)

Answer 2

Answer:

(8, -22)

Step-by-step explanation:

y = –4x + 10

y = –2x – 6

subtract the 2 eqns, u get:

y - y = -4x + 10 - (-2x - 6)

0 = -4x +10 + 2x + 6

4x - 2x = 10 + 6

2x = 16

x = 8

substitute x = 8 into y = –4x + 10

y = -4(8) + 10 = -32 +10 = -22

so ans is (8, -22)