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VMariaS [17]
3 years ago
8

Solve by using elimination. Express your answer as an ordered pair.

Mathematics
2 answers:
charle [14.2K]3 years ago
8 0

Answer:

(3, 5)

Step-by-step explanation:

Since none of the x y coeficcints are the same, we need to multiply entire equations

3(2x+5y=31)=6x+15y=93

2(3x-2y=-1)=6x-4y=-2

Now we have the same x coeficcionts!

(6x+15y=93)-(6x-4y=-2)=19y=95

we then divide 19 on both sides to get:

y=5

Now we know what y is,  we'll need to plug 5 in for y in the second equation.

3x-2(5)=-1

3x-10=-1

3x=9

x=3

Aloiza [94]3 years ago
6 0

Greetings again.

The answer is (3,5)

Explanation:

Other previous questions about the System of Two Variables Linear Equations. Previous questions, both y-terms have the same absolute-values but different operator/sign. Some questions previously have same operators as we multiply one of the equation by -1 to eliminate.

But this question, there are no terms that are same. Especially not the same looking value.

<em>And what do we do if it's like this?</em>

The answer is, do something to make both equations have same absolute value but different operators.

That is to multiply. For this question, I'll be eliminating x-term. So I'll multiply both equations to make the x-term have same absolute-value and different operator.

Because 2 and 3 can multiply into 6. Therefore, multiply the whole first equation by 3 and multiply the whole second equation by 2.

\left \{ {{2x+5y=31} \atop {3x-2y=-1}} \right. \\\left \{ {{2x(3)+5y(3)=31(3)} \atop {3x(2)-2y(2)=-1(2)}} \right. \\\left \{ {{6x+15y=93} \atop {6x-4y=-2}} \right.

This is our new equations. Since we need to eliminate x-term. We multiply one of the equation by -1. I'll choose the second equation to multiply.

6x(-1)-4y(-1)=-2(-1)\\-6x+4y=2

\left \{ {{6x+15y=93} \atop {-6x+4y=2}} \right.

Then proceed with add/subtract vertically

6x-6x = 0

15y+4y = 19y

93+2 = 95

Therefore, we get 19y = 95

19y=95\\y=\frac{95}{19} \\y=5

Our y-value is 5. However, we are not done yet. Since this is the System of Two Variables Linear Equation. We need to find the x-value too to express in ordered pairs. (x,y)

Choose any given equations to substitute y = 5 in. I'll substitute y = 5 in 3x-2y=-1

3x-2y=-1

Substitute y = 5 in the equation.

3x-2(5)=-1\\3x-10=-1\\3x=-1+10\\3x=9\\x=3

Thus, when y = 5, x = 3 or when x = 3, y = 5. As the ordered pairs = (x,y) Therefore, the answer is (3,5)

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