Solving Equations Using Substitution Quick Check

Question

3 of 53 of 5 Items

Question
Solve the system of equations.
3x+y=2

7x−4y=30
(1 point)
Responses

(2, −2)
left parenthesis 2 comma negative 2 right parenthesis

(2, −4)
left parenthesis 2 comma negative 4 right parenthesis

(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis

(12, 12)

Answer 1

To solve the system of equations using substitution, we have the following equations:

1. $3x+y=2$ (Equation 1)
2. $7x-4y=30$ (Equation 2)

Let's solve Equation 1 for $y$:

$$y=2-3x$$

Now we can substitute this expression for $y$ into Equation 2:

$$7x-4(2-3x)=30$$

Distributing the $-4$:

$$7x-8+12x=30$$

Combining like terms:

$$19x-8=30$$

Adding $8$ to both sides:

$$19x=38$$

Dividing both sides by $19$:

$$x=2$$

Now we substitute $x=2$ back into the expression for $y$:

$$y=2-3(2)=2-6=-4$$

Thus, the solution to the system of equations is:

$$(x,y)=(2,-4)$$

So the correct response is:

(2, −4)