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МатематикаВопрос:
Solve the system of equations: { x + 6y = 7 { 4y - x = 13
Ответ:
System of Equations:
- Equation 1: x + 6y = 7
- Equation 2: 4y - x = 13
Brief explanation: We will solve this system of linear equations using the substitution method. We will rearrange the second equation to solve for x and then substitute that expression into the first equation.
Step-by-step solution:
- Step 1: Rearrange Equation 2 to solve for x.
From Equation 2, we have: $$4y - x = 13$$. Adding x to both sides and subtracting 13 from both sides gives us: $$x = 4y - 13$$. - Step 2: Substitute the expression for x into Equation 1.
Substitute $$x = 4y - 13$$ into Equation 1: $$(4y - 13) + 6y = 7$$. - Step 3: Solve for y.
Combine like terms: $$10y - 13 = 7$$. Add 13 to both sides: $$10y = 20$$. Divide by 10: $$y = 2$$. - Step 4: Substitute the value of y back into the expression for x.
Using the expression from Step 1: $$x = 4y - 13$$. Substitute $$y = 2$$: $$x = 4(2) - 13$$. - Step 5: Calculate the value of x.
$$x = 8 - 13$$, so $$x = -5$$.
Answer: x = -5, y = 2
