Identify Equations: Identify the system of equations to solve. We have two equations: 1) 6x + 2y = -26 2) x - 6y = 21 We need to find the values of x and y that satisfy both equations simultaneously.Choose Solution Method: Choose a method to solve the system of equations. We can use either substitution or elimination. For this problem, we will use the elimination method because it allows us to eliminate one variable by adding or subtracting the equations.Multiply Second Equation: Multiply the second equation by 2 to make the coefficients of y in both equations equal in magnitude but opposite in sign. 2 * (x - 6y) = 2 * 21 This gives us a new equation: 2x - 12y = 42Add Equations to Eliminate y: Add the new equation from Step 3 to the first equation to eliminate y. (6x + 2y) + (2x - 12y) = -26 + 42 This simplifies to: 8x - 10y + 2y - 12y = 16 8x - 10y = 16

Grade 7

Solve equations involving like terms

Full solution

6x+2y=-26

x-6y=21

Choose easier equation: Step $1$ : Choose the easier equation to manipulate. Here, the second equation $x - 6y = 21$ seems simpler to isolate one variable. $\newline$ Isolate $x$ : $\newline$ $x = 6y + 21$
Substitute $x$ into first equation: Step $2$ : Substitute the expression for $x$ from Step $1$ into the first equation. $\newline$ $6(6y + 21) + 2y = -26$ $\newline$ $36y + 126 + 2y = -26$
Combine terms and solve for $y$ : Step $3$ : Combine like terms and solve for $y$ . $38y + 126 = -26$ $38y = -26 - 126$ $38y = -152$ $y = -152 / 38$ $y = -4$
Substitute $y$ back into $x$ : Step $4$ : Substitute $y = -4$ back into the expression for $x$ from Step $1$ . $\newline$ $x = 6(-4) + 21$ $\newline$ $x = -24 + 21$ $\newline$ $x = -3$