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2x + y = 1

3x + 4y = 14

Solve using substitution and elimination. Show and explain steps. HURRY PLS

User RamAlx
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1 Answer

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16 votes

We will explain both ways and show work of both. When we solve these equations, they are asking to find an intersection point.

Substitution: Make an equation equal to a variable, then plug this equation inside the other equation in the variable you made it equal to.

2x+y=1

3x+4y=14

1. We can make it equal to any variable, either x or y, and which ever equation, but let's make the first equation equal to y since it is much easier.

2x+y=1

-2x -2x

y=1-2x

2. Now that we rearranged this equation equal to y, let's plug this equation into the other equation in the y variable.

3x+4(1-2x)=14

3. Simplify and solve.

3x+4-8x=14 (Distribute the 4)

-5x+4=14 (Combine like terms)

-4 -4

-5x=10 (Isolate x)

x=-2

4. Plug in the x value into either equation to find the y coordinate.

x=-2

I'm going to plug this in the first equation.

2(-2)+y=1

-4+y=1

y=5

The answer is (-2,5)

Elimination: we get rid of one variable to easily get a x or y coordinate.

2x+y=1

3x+4y=14

How do we eliminate a variable? Think of this problem as an addition problem. Let's get rid of y since it looks easier. What multiplied by y plus the 4y in the row would make it equal to zero? This is eliminating the y variable.

1. By multiplying the first equation by negative 4, we will be able to eliminate y.

-4(2x+y=1)

3x+4y=14

2. Let's distribute.

-8x-4x=-4

3x+4y=14 (nothing is done to the second equation)

3. Add down.

-8x-4y=-4

3x+4y=14

_________

-5x+0=10

4. Solve for x

-5x=10

x=-2

5. Input the number in for an equation to get a coordinate.

I'm going to use the first equation since it's easier.

2(-2)+y=1

-4+y=1

y=5

The answer is (-2, 5)

User GaryX
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