Solve the system by substitution. {:[y=4x],[y=7x-30]:} (◻,◻)

Identify Equation to Substitute: First, we need to identify which equation to substitute into the other. Since the first equation is already solved for y, we can substitute the expression for y from the first equation into the second equation. Substitute y = 4x into the second equation y = 7x - 30.Substitute Expression for y: Now we have 4x = 7x - 30. To find the value of x, we need to solve this equation. Subtract 4x from both sides to get 0 = 3x - 30.Solve for x: Next, add 30 to both sides to isolate the term with x. 3x = 30.Isolate the Term with x: Now, divide both sides by 3 to solve for x. x = 30 / 3. x = 10.Find Value of x: We have found the value of x to be 10. Now we need to substitute this value back into one of the original equations to find the value of y. Let's substitute x = 10 into the first equation y = 4x.Substitute x into First Equation: Substitute x with 10 in the equation y = 4x. y = 4 * 10. y = 40.Calculate Value of y: We have found the value of y to be 40 when x is 10. This gives us the solution to the system of equations. The solution is (x, y) = (10, 40).

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Solve the system by substitution.

{:[y=4x],[y=7x-30]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{array}{l} y=4 x \\ y=7 x-30 \end{array}$ $\newline$ $(\square, \square)$

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Math Problems

Grade 8

Identify arithmetic and geometric sequences

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Q. Solve the system by substitution.

\newline

\begin{array}{l} y=4 x \\ y=7 x-30 \end{array}

\newline

(\square, \square)

Identify Equation to Substitute: First, we need to identify which equation to substitute into the other. Since the first equation is already solved for $y$ , we can substitute the expression for $y$ from the first equation into the second equation. $\newline$ Substitute $y = 4x$ into the second equation $y = 7x - 30$ .
Substitute Expression for y: Now we have $4x = 7x - 30$ . To find the value of $x$ , we need to solve this equation. Subtract $4x$ from both sides to get $0 = 3x - 30$ .
Solve for $x$ : Next, add $30$ to both sides to isolate the term with $x$ . $3x = 30$ .
Isolate the Term with x: Now, divide both sides by $3$ to solve for x. $\newline$ $x = \frac{30}{3}$ . $\newline$ $x = 10$ .
Find Value of x: We have found the value of $x$ to be $10$ . Now we need to substitute this value back into one of the original equations to find the value of $y$ . Let's substitute $x = 10$ into the first equation $y = 4x$ .
Substitute $x$ into First Equation: Substitute $x$ with $10$ in the equation $y = 4x$ . $\newline$ $y = 4 \times 10$ . $\newline$ $y = 40$ .
Calculate Value of $y$ : We have found the value of $y$ to be $40$ when $x$ is $10$ . This gives us the solution to the system of equations. $\newline$ The solution is $(x, y) = (10, 40)$ .