-x+y=2 3x-5y=-4 substituion method

Answer 1

To solve both variable, x and y; you will first need to solve ONE of the equations for a variable.

I will choose to solve -x+y=2 and solve for y, this is because this will keep all the numbers positive!

-x+y=2 ----> y=2+x

Now that we KNOW y = 2+x we will substitute "2+x" in for y in the OTHER equation!

So...

3x-5y=-4 ----> 3x-5(2+x) = -4

Now that we ONLY have one variable, we can solve for x!

First Distribute

3x-5(2+x) = -4 ----> 3x-10-5x = -4

Combine Like Terms!

3x-10-5x = -4 ----> -2x-10 = -4 ----> -2x = 6

Divide by -2 on both sides

x=-3

Now that we have solved x completely Plug in X=-3 into EITHER one of the two equations from the question(-x+y=2 OR 3x-5y=-4)

I will CHOOSE to use -x+y=2

Using x = -3, substitute -3 for x

-(-3) + y = 2

Distribute the negative

3+ y = 2

Combine like terms

y=-1

So now we have finished

Answers:

x=-3

y=-1

If you would like to CHECK your answer you an plug in Both x and y into the original equations and see if both sides are equal.

-x+y=2

-(-3) + (-1) = 2

3-1 = 2

2 = 2

Since 2=2 that means our answer are correct!

Answer 2

Hello Trace,

When solving a system of equations by the substitution method, you should look at the two equations and see which one has the easiest opportunity to set equal to x or equal to y.

In looking at the two equations

-x + y = 2

3x - 5y = -4

take the first equation and set equal to y. This way you deal with the minimum amount of coefficients greater than 1.

-x + y = 2

add x to both sides to get y by itself, it is called add the opposite

-x + x + y = 2 + x

simplifying

y = 2 + x

now substitute this equation for y into the second original equation

3x - 5(2+x)= -4 Now simplify and solve for x

3x - 10 -5x = -4

-2x - 10 =-4

-2x=-4+10

-2x=6

x=6/(-2)

x=-3

so substitute into y = 2 + x and solve for y

y = 2 + (-3) =-1

so X equals -3 and y = -1

Substitute into the second equation to verify that x and y are correct

3(-3) - 5(-1) =-4? True or false.

-9 +5 =-4 true

Answer 3

Wyzant

Algebra 1

Trace S. asked • 1d

-x+y=2 3x-5y=-4 substituion method

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Bao D. answered • 1d

Tutor 5 (1)

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To solve both variable, x and y; you will first need to solve ONE of the equations for a variable.

I will choose to solve -x+y=2 and solve for y, this is because this will keep all the numbers positive!

-x+y=2 ----> y=2+x

Now that we KNOW y = 2+x we will substitute "2+x" in for y in the OTHER equation!

So...

3x-5y=-4 ----> 3x-5(2+x) = -4

Now that we ONLY have one variable, we can solve for x!

First Distribute

3x-5(2+x) = -4 ----> 3x-10-5x = -4

Combine Like Terms!

3x-10-5x = -4 ----> -2x-10 = -4 ----> -2x = 6

Divide by -2 on both sides

x=-3

Now that we have solved x completely Plug in X=-3 into EITHER one of the two equations from the question(-x+y=2 OR 3x-5y=-4)

I will CHOOSE to use -x+y=2

Using x = -3, substitute -3 for x

-(-3) + y = 2

Distribute the negative

3+ y = 2

Combine like terms

y=-1

So now we have finished

Answers:

x=-3

y=-1

If you would like to CHECK your answer you an plug in Both x and y into the original equations and see if both sides are equal.

-x+y=2

-(-3) + (-1) = 2

3-1 = 2

2 = 2

Since 2=2 that means our answer are correct!

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Zolomon K. answered • 20h

Tutor 5 (7)

Passionate Math and Science Tutor | Experienced with K-12 Students

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Solve (-x + y = 2) & (3x - 5y = -4) using the substitution method:

Step 1: Simplify the easier equation (get either x or y alone on one side of the equation)

-x + y = 2

y = 2 + x

Step 2: Plug in your value into the other equation.

3x - 5(2 + x) = -4

Step 3: Simplify the equation until you get an answer (here we will get an x value, but if we solved for x instead of y in step 1, we would get a y value here).

3x - (10 + 5x) = -4

3x - 10 - 5x = -4

-2x - 10 = -4

-2x = 6

x = -3

Step 4: Plug the x value (-3) into one of the equations to solve for y

-x + y = 2

-(-3) + y = 2

3 + y = 2

y = -1

Step 5: Check if your answers are correct by plugging x and y into both equations (x = -3, y = -1).

Equation 1

-x + y = 2

-(-3) + (-1) = 2

3 - 1 = 2

2 = 2

CORRECT

Equation 2

3x - 5y = -4

3(-3) - 5(-1) = -4

-9 + 5 = -4

-4 = -4

CORRECT

Step 6: State your answer

x = -3

y = -1

Answer 4

Solve (-x + y = 2) & (3x - 5y = -4) using the substitution method:

Step 1: Simplify the easier equation (get either x or y alone on one side of the equation)

1. -x + y = 2
2. y = 2 + x

Step 2: Plug in your value into the other equation.

1. 3x - 5(2 + x) = -4

Step 3: Simplify the equation until you get an answer (here we will get an x value, but if we solved for x instead of y in step 1, we would get a y value here).

1. 3x - (10 + 5x) = -4
2. 3x - 10 - 5x = -4
3. -2x - 10 = -4
4. -2x = 6
5. x = -3

Step 4: Plug the x value (-3) into one of the equations to solve for y

1. -x + y = 2
2. -(-3) + y = 2
3. 3 + y = 2
4. y = -1

Step 5: Check if your answers are correct by plugging x and y into both equations (x = -3, y = -1).

1. Equation 1
2. -x + y = 2
3. -(-3) + (-1) = 2
4. 3 - 1 = 2
5. 2 = 2
6. CORRECT
7. Equation 2
8. 3x - 5y = -4
9. 3(-3) - 5(-1) = -4
10. -9 + 5 = -4
11. -4 = -4
12. CORRECT

Step 6: State your answer

1. x = -3
2. y = -1

Answer 5

Answer 6

There are different ways to solve this system of equations by using the substitution method since we have to choose one variable in any of the equations. To solve a system of equations means that we will find the values of the variables that satisfy the equations (will make them true statements). Of course, we will select the variable that is easier to isolate (positive and with the lowest possible coefficient) In this case I opted for y in the first equation:

-x+y=2 to isolate y we add x on both sides of the equation and simplify.

y=2+x (-x+x=0)

The next step will be to substitute (replace) the value of y from the new equation we got into the second given.

3x-5y=-4 will be written as 3x-5(2+x)=-4

By doing this our new equation is written in terms of only one variable, x. Then we will simplify the left side of the equation by following the properties we have studied in this respect.

3x-5(2+x) can be expressed as 3x-10-5x or as -2x-10 here we used distributive property to multiply and add.

Now our new equation will look like this: -2x-10= -4

+10 +10

Adding 10 on both sides of the equation will allow us to eliminate the 10 that is subtracting. Now the equation will be: -2x=6 (-10+10=0 and -4+10=6)

If we divide both sides of our equation by -2 we can now isolate x and therefore get its value

-2x = 6 simplifying this we will get x = -3. We now found the value of the first variable.

-2 -2

To find the value of y (the second variable) we will substitute the value of x in any of the original equations given in this exercise. Then we will solve the resultant equation which now will be in terms of only one variable, y. I chose the equation -x+y=2 (the one with smaller numbers)

-x+y=2 by substituting x by its value we get:

-(-3)+y=2 or 3+y=2 (negative times negative turns positive)

We now subtract 3 on both sides of the equation to isolate y on the left side:

y=2-3 or y=-1 (the value of the second variable)

We have solved the system, but it is very important to verify our answers (they must satisfy any of the originally given equations)

3x-5y=-4 with the values we found will be: 3(-3)-5(-1)=-4 ? Simplifying: -9+5=-4