use substitution to solve?

Question

-2x+7y=10
x-3y=-3

Answer 1

Notice x = -3 + 3y (based on your second equation), so substitute this for x into your first equation to solve for y:

-2x + 7y = 10

-2(-3 + 3y) + 7y = 10

6 - 6y + 7y = 10

6 + y = 10

y = 4

Now plug this into the other equation to solve for x:

x = -3 + 3y

x = -3 + 3(4)

x = -3 + 12

x = 9

ANSWER: x=9, y=4

NRT

Answer 2

From the given linear system with two unkowns, i.e.
[eqn1]      -2x + 7y = 10
[eqn2]      x - 3y = -3,

we notice that from [eqn2], we can express x as follows:
[eqn3]      x = 3y - 3.

By plugging [eqn3] to [eqn1] we get
-2(3y - 3) + 7y = 10.

From this equation, we can solve for y as follows
        -6y + 6 + 7y = 10
        -6y + 7y = 10 - 6
[eqn4]     y = 4.

Using the information for y in [eqn4], we plug this to [eqn3] to obtain the value for x. That is,
        x = 3(4) - 3
        x = 12 - 3
        x = 9.

Therefore, pair x = 9 and y = 4 satisfies that given linear system of two unknowns defined in [eqn1] and [eqn2].

Answer 3

-2x+7y=10
x-3y=-3

equate x
x-3y=-3
x=3y-3
subst. for x in:
-2x+7y=10
-2(3y-3) + 7y=10
-6y + 6 + 7y =10
6 + y =10
y =10-6
y=4
solve for x
x - (3(4))= -3
x -12 = -3
x =9

Check
-2x+7y=10
-2(9) + 7 (4) = 10
-18 + 28 = 10
10 = 10

Answer 4

You need to solve for one variable of choice and then substitute the value of that variable into the other equation.

LOOK:

For x - 3y = - 3, I will solve for x by adding 3y to BOTH sides of the equation.

We have this:

x = 3y - 3

I will plug 3y - 3 into -2x + 7y = 10 to find y.

Here we go:

-2(3y-3) + 7y = 10

Next: Multiply every term inside the parentheses by the outside
-2. See it?

We get:
-3y + 6 + 7y = 10

Next: combine like terms on the LEFT SIDE of the equation.

We get this:

4y + 6 = 10

4y = 10 - 6

4y = 4

y = 1.

Next:

Select one of the ORIGINAL EQUATIONS given to you and plug y to find the value of x.

I decided to pick x - 3y = -3.

Here it is:

x - 3(1) = -3

x - 3 = -3

x = 0

Solution and final answer is: {x = 0, y = 1}

Guido

Answer 5

-2x+7y=10
x-3y=-3

Solve for x in equation 1

x= 3y-3

then plug in the x into the first equation

-2(3y-3) + 7y = 10
-6y + 6 + 7y = 10
y + 6 = 10
y = 4.

Plug in y back into equation 2 and you will get what x equals.

x - 3(4) = -3
x - 12 = -3
x = 9

y = 4, x = 9

Answer 6

(1) -2x+7y=10
(2) x-3y=-3 (2a) x=3y-3
substitute (2a) into (1)
-2(3y-3)+7y=10
-6y+6+7y=10
y=4
from (2a)
x=3*4-3=12-3=9
x=9
y=4

Answer 7

x - 3y = -3
Add 3y to each side
x = 3y - 3
Replace x with 3y-3 in the first equation
-2(3y-3) + 7y = 10
-6y + 6 + 7y = 10
y + 6 = 10
y = 4
x = 3y - 3 = 3(4) - 3 = 12 - 3 = 9
Answer: (9,4)

Answer 8

x = 3y - 3
Put this into the first equation and solve for y. Then go back to x = 3y - 3 to find x.

Answer 9

1. you can use elimination: multiply the second equation by 2: 2x-6y=-6, and then add the two equations and get: 4y=7

2. or you can use subtitution: x=-3+3y is subtituted in the first equation.

Good Luck.