Question
Solve the system of equations by elimination :
5X + 6Y = - 6
7X - 3Y = - 54
Hint:
HINT: Perform any arithmetic operation and then find.
The correct answer is: x = - 6 and y = 4
Complete step by step solution:
Let 5x + 6y=-6…(i)
and 7x - 3y = - 54….(ii)
On multiplying (ii) with 2, we get 2(7x - 3y = - 54)
⇒14x - 6y = - 108…(iii)
Now, we have the coefficients of y in (i) and (iii) to be the same.
On adding (i) and (iii),
we get LHS to be 5x + 6y + 14x - 6y = 19x
and RHS to be - 6 + - 108 = - 114
On equating LHS and RHS, we have 19x = - 114
⇒x = - 6
On substituting the value of x in (i), we get 5× - 6 + 6y = - 6
⇒ - 30 + 6y = - 6
⇒ 6y = - 6 + 30
⇒ 6y = 24
⇒ y = 4
Hence we get x = - 6 and y = 4
Note: We can also solve these system of equations by making the coefficients of
to be the same in both the equations.
Related Questions to study
An international food festival charges for admission and for each sample of food. Admission and 3 samples cost $ 5.75. Admission and 6 samples cost $ 8.75. Write a linear function that represents the cost ,y , for any number of samples x?
An international food festival charges for admission and for each sample of food. Admission and 3 samples cost $ 5.75. Admission and 6 samples cost $ 8.75. Write a linear function that represents the cost ,y , for any number of samples x?
Use Substitution to solve each system of equations :
Y = 2X - 4
3X - 2Y = 1
Use Substitution to solve each system of equations :
Y = 2X - 4
3X - 2Y = 1
The graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered. What is the constant rate of change? What does it represent ? What is the initial value ? What might that represent?
The form of a linear equation is y = mx + b in the slope-intercept notation. Variables in the equation are the X and Y. The values m and b represent the line's slope (m) and the value of y when x is 0 and Y is 500. (b). Because the line crosses the y-axis at (0,y), when x is 0, y is referred to as the y-intercept. A two-variable linear equation can be thought of as a linear relationship between y and x or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, x is referred to be an independent variable and y as a dependent variable because it depends on the x variable.
Often plotted along the horizontal axis represents the independent variable, x label or not. The majority of linear equations are functions. Alternatively, there is just one value of y for every value of x. You can calculate the value of the dependent variable, y, once the independent variable, x, has been given a value.
The graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered. What is the constant rate of change? What does it represent ? What is the initial value ? What might that represent?
The form of a linear equation is y = mx + b in the slope-intercept notation. Variables in the equation are the X and Y. The values m and b represent the line's slope (m) and the value of y when x is 0 and Y is 500. (b). Because the line crosses the y-axis at (0,y), when x is 0, y is referred to as the y-intercept. A two-variable linear equation can be thought of as a linear relationship between y and x or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, x is referred to be an independent variable and y as a dependent variable because it depends on the x variable.
Often plotted along the horizontal axis represents the independent variable, x label or not. The majority of linear equations are functions. Alternatively, there is just one value of y for every value of x. You can calculate the value of the dependent variable, y, once the independent variable, x, has been given a value.
