Chapter 4: Q. 4.14 (page 377)

Solve the system by substitution: $\{\begin{cases} 2 x + y = - 1 \\ 4 x + 3 y = 3 \end{cases}$

Short Answer

Expert verified

The solution of the system of equations is $(- 3, 5)$ .

Step by step solution

Step 1. Given Information.

The system of equations is $\{\begin{cases} 2 x + y = - 1 \\ 4 x + 3 y = 3 \end{cases}$ .

Step 2. Solve one of the equations for either variable.

We'll solve for the first equation for y,

$2 x + y = - 1$

$y = - 2 x - 1$

Step 3. Substitute the expression from Step 2 into the other equation.

We replace y in the second equation with the expression $- 2 x - 1$ .

$4 x + 3 y = 3$

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

Step 4. Solve the resulting equation.

Now we have an equation with just one variable.

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

$4 x - 6 x - 3 = 3$

$- 2 x = 6$

$x = - 3$

Step 5. Substitute the solution from Step 4 into one of the original equations to find the other variable.

We'll use the first equation and replace $x$ with $- 3$

2 x + y = - 1

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

$- 6 + y = - 1$

$y = 5$

Step 6. Write the solution as an ordered pair.

The ordered pair is $(x, y) .$

$(- 3, 5)$

Step 7. Check that the ordered pair is a solution to both original equations.

Substitute $x, y = - 3, 5$ into both equations and make sure they are both true.

$2 x + y = - 1$

$2 (- 3) + 5 = - 1$

$- 1 = - 1$

And, $4 x + 3 y = 3$

$4 (- 3) + 3 (5) = 3$

$- 12 + 15 = 3$

$3 = 3$

Both equations are True.

The point

(- 3, 5)

is the solution to the system.

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Solve the system by substitution: $\{\begin{cases} 2 x + y = - 1 \\ 4 x + 3 y = 3 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve one of the equations for either variable.

Step 3. Substitute the expression from Step 2 into the other equation.

Step 4. Solve the resulting equation.

Step 5. Substitute the solution from Step 4 into one of the original equations to find the other variable.

Step 6. Write the solution as an ordered pair.

Step 7. Check that the ordered pair is a solution to both original equations.

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Solve the system by substitution:2x+y=-14x+3y=3

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve one of the equations for either variable.

Step 3. Substitute the expression from Step 2 into the other equation.

Step 4. Solve the resulting equation.

Step 5. Substitute the solution from Step 4 into one of the original equations to find the other variable.

Step 6. Write the solution as an ordered pair.

Step 7. Check that the ordered pair is a solution to both original equations.

One App. One Place for Learning.

Most popular questions from this chapter

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Solve the system by substitution: $\{\begin{cases} 2 x + y = - 1 \\ 4 x + 3 y = 3 \end{cases}$