Question

51 leah is using substitution method to solve the system of equations below. what should the first step be? you do not need to solve the system.

$y = 3x$
$-2x + 8y = -2$

52 paula is using elimination method to solve the system of equations below. what should the first step be? you do not need to solve the system.

$4x + 3y = 7$
$2x - 9y = 35$

53 when using elimination method to solve the system of equations below, what should the first step be? you do not need to solve the system.

$5x + 6y = 2$
$-5x + 10y = -50$

Explanation:

Question 51

Step1: Recall Substitution Method

The substitution method involves replacing one variable with its expression from another equation. Here, we have \( y = 3x \) and \( -2x + 8y=-2 \).

Step2: Identify Substitution

Since \( y \) is already expressed in terms of \( x \) (\( y = 3x \)), the first step is to substitute \( y = 3x \) into the second equation \( -2x + 8y=-2 \). So substitute \( y = 3x \) into \( -2x + 8y=-2 \).

Step1: Recall Elimination Method

The elimination method aims to eliminate a variable by making coefficients of one variable equal (or opposite) in both equations. Here, equations are \( 4x + 3y = 7 \) and \( 2x - 9y = 35 \).

Step2: Choose Variable to Eliminate

To eliminate \( x \), we can multiply the second equation \( 2x - 9y = 35 \) by 2 (to make the coefficient of \( x \) equal to 4, same as in the first equation). Or to eliminate \( y \), multiply first equation by 3 (to make coefficient of \( y \) equal to 9, opposite sign can also be considered). A common first step is to multiply the second equation \( 2x - 9y = 35 \) by 2 to get \( 4x-18y = 70 \), so that we can eliminate \( x \) by subtracting or adding. So multiply \( 2x - 9y = 35 \) by 2.

Step1: Recall Elimination Method

Elimination method uses adding or subtracting equations to eliminate a variable. Here, equations are \( 5x + 6y = 2 \) and \( -5x + 10y=-50 \).

Step2: Identify Opposite Coefficients

The coefficient of \( x \) in first equation is 5 and in second is -5, which are opposites. So the first step is to add the two equations together to eliminate \( x \). So add \( 5x + 6y = 2 \) and \( -5x + 10y=-50 \).

Answer:

Substitute \( y = 3x \) into \( -2x + 8y=-2 \)

Question 52